There were new kidnappings this weekend, bringing to at least trying to drive coalition forces out of Iraq.
A senior U.S. commander said the military intends to take back Fallujah and other rebel areas by year's end.
"We need to make a decision on when the cancer of Fallujah is going to be cut out," the unnamed commander told The New York Times, adding that operations could begin in November or December.
In another sign of continuing instability 17 months into the U.S.-led occupation of Iraq, a suicide car bomb killed three people in Samarra - a northern city that U.S. and Iraqi commanders have portrayed as a success story in their attempts to put down the insurgency.
Over the past week, about 300 people have been killed in escalating violence, including bombings, street fighting and U.S. air strikes. Last week, U.N. Secretary-General Kofi Annan warned there could not be "credible elections if the security conditions continue as they are now."
But Iraqi Prime Minister Ayad Allawi, who spoke with reporters after a meeting with British leader Tony Blair in London, said his interim government was determined "to stick to the timetable of the elections," which are due by Jan. 31.
"January next, I think, is going to be a major blow to terrorists and insurgents," said Allawi, who is heading to the United Nations for this week's General Assembly session. "We are adamant that democracy is going to prevail, is going to win in Iraq."
Allawi also said that ousted Iraqi leader Saddam Hussein and his lieutenants would go on trial soon. "Roughly speaking, I think October," Allawi said in a broadcast interview.
He said he did not think the trial would take long because the evidence against Saddam was "overwhelming."
President Bush is still confident the situation is improving but other high profile Republicans say its going to take more resources and a lot more time.
"I find it shocking that some people are surprised by the fact that it is a long and difficult conflict," Sen. John Kyl, a Republican from Arizona, said on CBS's "Face the Nation." "Hand-wringing does not win wars."
"Hand-wringing" is the new catch phrase conservatives use to those who question the president's strategy, reports CBS News Correspondent Joie Chen. But it drew a sharp rebuke from one key Republican.
"The term 'hand-wringing' is a little misplaced here," said Sen. Chuck Hagel, a Vietnam War veteran who is co-chairman of President Bush's re-election committee in Nebraska. "A crisp, sharp analysis of our policies are required. We didn't do that in Vietnam, and we saw 11 years of casualties mount to the point where we finally lost."
Hagel's remarks were echoed by another Vietnam vet, who added an unwelcome suggestion about what might be needed in Iraq: more American help.
"We need to make plans for an enlarged army and an enlarged marine corps," said Sen. John McCain, an Arizona Republican, in a broadcast interview. "It may be as many as 70,000 army and 20,000-25,000 Marines."
Baghdad showed off one return to normalcy, the first Iraqi Airways flights in 14 years. It could bring business people, but it may be more popular with people getting out, afraid to stay in a country where no city and no street now seems safe, reports CBS News Correspondent Barry Petersen.
Allawi, a Sunni Muslim, has been insistent about holding elections on time because of pressure from Iraq's Shiite Muslim community and its most powerful cleric, Grand Ayatollah Ali al-Sistani, who fought for early elections. Reneging on the vote would risk angering the generally cooperative Shiite religious establishment.
Shiites, who are in the majority in Iraq, are eager to translate their numbers into political power.
But alongside the increasing violence, several cities in the Sunni Muslim heartland north and west of Baghdad are out of U.S. and Iraqi government control, with insurgents holding sway, particularly in the city of Fallujah. That raises questions on whether balloting can be held there - and the legitimacy of elections held without adequate Sunni participation.
The decapitated bodies of the three slain Kurdish hostages were found on a road near the northern city of Mosul, said Sarkawt Hassan, security chief in the Kurdish town of Sulaimaniyah. He said the three were members of the peshmerga militia of the Kurdistan Democratic Party.
The videotape, posted Sunday on a site known for its Islamic militant content, shows three young men, two of whom hold up identity cards. Seconds later, each has his throat slit and his head placed on the back of his body.
The Ansar al-Sunna Army - a Sunni militant group that said it killed 12 Nepalese hostages in August and carried out Feb. 1 suicide attacks against Kurdish political parties that killed 109 people - claimed responsibility for the beheadings in a statement with the video.
It said the three were KDP members snatched as they were transporting military vehicles to a base in Taji, 15 miles north of Baghdad.
The group said it was targeting Iraqi Kurdish parties because they have "sworn allegiance to the crusaders and fought and are still fighting Islam and its people."
The tape and the statement could not be independently verified.
Later, the Arab news station Al-Jazeera aired a separate video claiming 18 captured Iraqi soldiers would be killed unless a detained aide of rebel Shiite cleric Muqtada al-Sadr was freed in 48 hours. The men in military dress were shown seated at gunpoint in the video from a group calling itself the Brigades of Mohammed bin Abdullah.
No audio was aired, but Al-Jazeera's announcer said the militants threatened to kill the 18 unless Hazem al-A'araji, who was detained in a raid by U.S. and Iraqi forces on al-Sadr's Baghdad offices on Saturday, is freed.
The videos surfaced the day before the Tawhid and Jihad group, led by Jordanian terror mastermind Abu Musab al-Zarqawi, has threatened to behead Americans Jack Hensley and Eugene Armstrong and Briton Kenneth Bigley, who were seized from their Baghdad house last week.
The group, which has claimed responsibility for a series of bombings and hostage takings, demands the release of Iraqi women from the American controlled Abu Ghraib and Umm Qasr prisons.
Abu Ghraib is the prison where U.S. soldiers were photographed sexually humiliating male prisoners, but the U.S. military says no women are held at either facility, though it says it is holding two female "security prisoners" elsewhere.
More than 100 foreigners have been kidnapped in Iraq, some for lucrative ransoms, and many have been executed. At least five other Westerners are currently being held hostage here, including an Iraqi-American man, two female Italian aid workers and two French reporters.
Lebanon's Foreign Ministry said Sunday that three Lebanese men and their Iraqi driver were abducted by gunmen on the Baghdad-Fallujah highway Friday night. The four worked for a travel agency that has a branch in Baghdad, a Foreign Ministry official said
Sunday's attack in Samarra, 65 miles north of Baghdad, came less than a week after American forces re-entered the city, which had been under insurgents' control and a virtual "no-go" area for U.S. troops since May 30.
The Americans returned under a peace deal brokered by tribal leaders under which U.S. forces agreed to provide millions of dollars in reconstruction funds in exchange for an end to attacks on American and Iraqi troops.
The blast killed an Iraqi soldier, a civilian and the suicide bomber and wounded four American and three Iraqi soldiers, said Maj. Neal O'Brien of the Army's 1st Infantry Division.
Allawi has pointed to the Samarra deal as an example of success in a fight he insists U.S and Iraqi forces are winning against the insurgents.
"We are squeezing out the insurgency," he said in a broadcast interview. "We have secured Samarra now, which was an important tie for insurgencies and the so-called resistance."
Meanwhile, U.S. warplanes and artillery pounded the insurgent stronghold of Fallujah late Saturday and early Sunday, killing four people and wounding six, hospital officials said. The military said it hit a checkpoint manned by militants linked to al-Zarqawi, the military said.
Elswhere, four insurgents were killed when a bomb they were attempting to plant at the side of a road near the eastern Iraqi city of Suwayrah exploded shortly before midnight Saturday, a military spokesman said.