ISLAMABAD - Afghan President Hamid Karzai arrived in Pakistan's capital on a trip widely believed to be aimed at seeking Islamabad's help in ending a decade-old Taliban insurgency.

According to a senior Pakistani security official, Karzai has told the U.S. that "seeking a military victory in Afghanistan will remain a futile venture without a stepped-up political dialogue with the Taliban."

The Pakistani security official (who spoke Friday to CBS News on condition of anonymity) repeated a widely-held belief among the country's armed forces and the intelligence community that "there is no way out of the Afghan quagmire without a political settlement which involves the Taliban agreeing to give up their fight in return for a slice of the political pie."

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Some members of President Obama's newly appointed national security team believe American troops should be pulled out of Afghanistan more rapidly than previously discussed, according to a report in The New York Times.

Officials from the military and the Obama administration, who spoke to the Times on condition of anonymity because the president is still deciding how big a troop reduction is wise for this summer, said new "strategic considerations" had prompted the revised thinking.

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Of the many adjectives used to describe Mullah Mohammed Omar, the one-eyed leader of the Taliban in Afghanistan and elsewhere, the most apt is probably "elusive."

On Monday, Afghan and, later, international media began churning out reports that Omar had been killed. He had been out of contact with his commanders for several days and reportedly was shot while being moved inside Pakistan with the help of a former Pakistani intelligence official.

A Taliban spokesman countered that Omar was alive and was somewhere inside Afghanistan.

The is-he-or-isn't-he rumors are nothing new in Afghanistan, where reports of Omar's demise have sprung up repeatedly, even occasionally coming from credible sources within the country's government. There is currently no evidence that he's dead but no official - Afghani or Western - has seen him in a very long time, raising the question: Who, exactly, is Mullah Omar?

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During his third deployment to Afghanistan, Australia's Sgt. Brett Wood was killed by an improvised explosive device on Monday while patrolling on foot. He was the 24th Australian soldier killed in combat in Afghanistan.

Wood will most likely be remembered by U.S. forces for his actions in 2006 that earned him Australia's Medal of Gallantry, the country's third-highest honor for battlefield valor.

Wood was leading a team in a platoon working with a U.S. company from the 10th Mountain Division clearing an insurgent sanctuary in Chora Valley when the Americans came under rocket and small arms fire, according to his medal citation. The Australians were caught in thick vegetation when four rockets landed on them, injuring Wood's foot, knee and hand, the Australian Broadcasting Corporation reports.

Then-corporal Wood didn't tell his commander he'd been wounded when he obeyed his leader's order to charge forward, the citation states.

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As the years went by with no capture of Osama bin Laden, a popular image developed of an ailing, out-of-touch ascetic living a harsh, spartan existence in the mountainous Afghan-Pakistan border region.

The comedienne Joan Rivers had this gag: The way to find Osama bin Laden in Afghanistan was to locate the only extension cord in the country and follow it to his dialysis machine.

But data from intelligence gathered in last Sunday's raid on bin Laden's Abbbottabad compound paints a picture of bin Laden as more active and engaged in al Qaeda's terrorist activities than the ascetic cave-dweller image would indicate.

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Last updated: 3:15 pm ET

The United States is in a tough spot when it comes to producing evidence of Osama bin Laden's death. The government claims that it has positively identified bin Laden through DNA analysis and facial recognition. But, there will be a clamor in some corners for pictures of the body. Pictures of Abu Musab al-Zarqawi, the former head of al Qaeda in Iraq, were released after he was killed, as were the pictures of the two sons of Saddam Hussein after their deaths at the hands of U.S. troops.

Complete coverage: The Death of Osama bin Laden

But, bin Laden's case is touchier. The U.S. government doesn't want to do anything to enhance the now former al Qaeda leader's mythological standing in the radical Islamic world. His death picture would become instant fodder for radical Jihadist websites and undoubtedly a recruiting tool.

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A former Taliban ambassador to Pakistan, who held the post on Sept. 11, 2001, tells CBS News the U.S. military's killing of Osama bin Laden will only stoke anti-American sentiment in the Muslim world, and the al Qaeda leader's death will "not be acceptable to any Muslim."

"I think this will increase the problem" for Americans, Abdul Salam Zaeef told CBS News in an interview from the Afghan capital.

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Pakistan's leadership is encouraging Afghan President Hamid Karzai to scale back Afghanistan's relationship with the United States and look instead to a strategic partnership with its neighbors to the east, the Wall Street Journal reports.

Pakistani Prime Minister Yousuf Raza Gilani made the pitch at an April 16 meeting, telling Karzai that the U.S. had failed both countries, the Journal reports, citing Afghan sources.

"Mr. Karzai is wavering on Pakistan's overtures, according to Afghans familiar with his thinking, with pro- and anti-American factions at the presidential palace trying to sway him to their sides," the Journal reports.

The U.S. is facing serious diplomatic hurdles with both countries. It faces continuing instability in Afghanistan -- where this week hundreds of Taliban militants were set free from a Kandahar prison, and where the U.S. is eyeing replacing controversial ambassador Karl Eikenberry with diplomat Ryan Crocker -- despite a decade-long military presence there. In Pakistan, a U.S. contractor working for the CIA was held on murder charges, causing a high-level international stir. Leaked documents also revealed this week that the U.S. considers Pakistan's spy agency, the ISI, a terror group similar to Hamas or Hezbollah.

The majority of U.S. and coalition troops are set to be withdrawn from Afghanistan beginning this summer, and "the country's neighbors, including Pakistan, Iran, India and Russia, are beginning to jockey for influence, positioning themselves for Afghanistan's post-American era," the Journal reports.

This story was written by CBS News Washington bureau chief Christopher Isham

Chairman of Joint Chiefs of Staff Admiral Michael J. Mullen continued his whirlwind tour of conflict zones today -- starting the day at dawn in Islamabad, touching down in Kabul, for several hours and ending the day in Baghdad, Iraq.

Following a series of very tough interviews with the Pakistani media in which he made it very clear that he was not happy with the connections between the Afghan insurgent group known as the Haqqani network and the Pakistani intelligence service--the ISI, Adm Mullen met one-on-one with Pakistani army chief of staff, General Ashfaq Kiyani until 2 a.m.

Mullen: We cannot let the Pakistan relationship come apart

In an interview today aboard his aircraft, Mullen told reporters that the meeting with Kiyani went well and that the two men were able to work through the difficult issues between the two countries because of the underlying strength of the relationship. He said that despite recent tensions, the military relationship with the Pakistani military remains very strong and that coordinated campaigns in the northeastern Afghanistan had been very effective in routing insurgents on both sides of the border. According to another senior U.S. military official, U.S. military assistance to Pakistan is on track to reach $3 billion this year.

In Kabul, Mullen met with General David Petreaus and other U.S. commanders as well as Afghan President Hamid Karzai. Mullen was generally upbeat about the military progress on the battlefield in Afghanistan, pointing to successes in southern part of the country, particularly the provinces of Kandahar and Helmand, which he visited earlier in the week. Mullen is also encouraged by the emerging units of the Afghan Local Police -- pro-government, village based police forces that are beginning to take control of security in some districts that were previously dominated by the Taliban. He repeated Petraeus' warning, however that the gains remain "fragile and reversible."

Mullen arrived late Thursday in Baghdad for meetings with Iraqi Prime Minister Nouri al Maliki and other Iraqi officials. At the top of the agenda is the scheduled departure of all U.S. troops at the end of this year and whether Iraqi security forces are prepared to handle the persistent, albeit radically reduced security challenges. Officials including Defense Secretary Robert Gates have said that the U.S. would consider extending the U.S. military presence, if requested to so by the Iraqis. To date, no such request has been forthcoming. Admiral Mullen said that he would "engage" the Iraqi leadership on this question.

Christopher Isham, Washington bureau chief for CBS News, filed this report from Islamabad, Pakistan

The Chairman of the Joint Chiefs of Staff Adm. Michael J. Mullen arrived in Pakistan Wednesday like a messenger in a storm bearing a clearly mixed message -- that the United States is profoundly upset by the continuing attacks on U.S. soldiers by Pakistan-based, and perhaps supported, insurgents but that the relationship between the two countries is much too important to abandon.

In interviews with U.S. and Pakistani reporters, Mullen said that the relationship between the Pakistani intelligence service, the Inter-Services Intelligence (ISI), and the Afghan insurgent group known as the Haqqani network, was at the "core" of the problems between the U.S. and Pakistan.

Before arriving in Pakistan, Mullen travelled to eastern and southern Afghanistan meeting with U.S. and coalition commanders who detailed both the progress on the battlefield and the persistent American casualties. One senior U.S. military officer carries with him a stack of 121 cards, each with the photograph and name of the troops killed under his command in the past year alone--deaths that he attributed to the Haqqani network.

Mullen stressed that it was his "sacred duty" as America's most senior military officer to represent in the strongest terms possible his objection to any support that is being provided to the Haqqani group by Pakistani intelligence.

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A report by the Department of Defense Inspector General casts doubt on the accuracy of the article in Rolling Stone magazine which cost Gen. Stanley McChrystal his job as the top commander in Afghanistan.

"Not all the events at issue occurred as reported in the article," the report says. "In some instances, we found no witness who acknowledged making or hearing the comments as reported."

Specifically, the investigation could not confirm quotes attributed to "sources familiar" with a meeting between the president and the Pentagon brass at which McChrystal thought the then newly elected president looked "uncomfortable and intimidated," and it could not confirm quotes attributed to "an adviser" stating that McChrystal was "pretty disappointed" with the president after a one-on-one meeting with the commander-in-chief.

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A special report published online and appearing in this week's issue of Rolling Stone - including extremely graphic photos and videos never before released - examines a group of U.S. Army soldiers who participated in the slayings of innocent Afghan civilians, and those who condoned, ignored or blew the whistle on their actions.

The Pentagon has sought to characterize the actions of members of the 3rd Platoon, Bravo Company who participated in atrocities as those of a "rogue unit" operating outside of their superiors' knowledge. Last week, a U.S. soldier pleaded guilty in the murders of three unarmed Afghan civilians, and of having participated in a conspiracy among several platoon members to execute innocents and then fake the crime scenes to appear that they were insurgents. Spc. Jeremy Morlock, 22, was court-martialed and sentenced for up to 24 years in prison.

Morlock's sentence was reduced in exchange for his testimony against other members of the "kill team" implicated in the executions that occurred in Kandahar province in January, February and May 2010.

No officers have been charged in the killings.

In "The Kill Team," Rolling Stone's Mark Boal writes that a review of internal Army records and investigative files, including military investigators' interviews with members of Bravo Company, indicates that a dozen infantrymen were operating openly, their clearly illegal actions common knowledge by "pretty much the whole platoon," according to one soldier who complained of them.

What is revealed in the article - and in the previously unreleased (and extremely graphic) pictures and video posted of the Kill Team's victims - is a culture of barbaric violence fueled by rage, boredom, revenge, drugs, and an unwavering antipathy to all Afghan civilians, even those with no obvious connection or loyalty to the Taliban.

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While Libya, Bahrain and other Middle East nations have become embroiled in unrest, stirring concerns about the role of American diplomacy and military force in the region, the U.S. has quietly begun to pull its forces out of a remote area of Afghanistan's Kunar Province, once declared to be key to its military campaign against al Qaeda and the Taliban.

Reporting in The New York Times, C.J. Chivers, Alissa J. Rubin and Wesley Morgan write that the withdrawal from the Pech Valley, which began on February 15, demonstrates a change - deploying Western forces in more populated areas while leaving Afghan forces to secure more remote regions.

The move, they write, is a test of the Afghans' military readiness while also protecting Afghan civilians.

According to the Times, at least 103 U.S. soldiers have died in or near the Pech Valley, and many more severely wounded, since the U.S. began its military campaign.

"I don't want the impression we're abandoning the Pech," said Maj. Gen. John F. Campbell, commander for eastern Afghanistan. "I prefer to look at it as realigning to provide better security for the Afghan people."

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General David Petraeus, the top U.S. and NATO commander in Afghanistan, says he is excepting a brutal fight in the spring when Taliban insurgents try to return from their winter safe havens to areas already cleared by the international forces.

"When you have 110,000 more of us than we had a year ago, we're obviously in many, many more places," he said in an interview with NATO TV. "We have taken away areas that matter to the Taliban and they have to fight back."

U.S., Afghan Forces Brace for Spring Offensive
CBS News Special Report: Afghanistan

But he doesn't see more violence as mission failure.

"When you're on the offensive... the insurgents have to fight back and violence goes up, it's a necessary part of any counter-insurgency."

Last year was the deadliest for American troops in the 10 year war, with 499 service members dying in the line of duty.

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