"To fulfill the promise that we have been made, we are hoping that NATO will come to Afghanistan before the elections of September," he said Monday at a news conference with Defense Secretary Donald H. Rumsfeld.
Karzai was delivering a speech to a joint meeting of Congress on Tuesday before meeting with President Bush at the White House.
NATO already is commanding the International Security Assistance Force in Kabul, the Afghan capital, as well as a reconstruction operation in the northern city of Kunduz. The alliance has pledged to expand its security operations to cities elsewhere in the war-torn country this summer.
Karzai and Rumsfeld addressed reporters beside a memorial plaque on a section of the Pentagon's western wall, where American Airlines Flight 77 slammed into the building on Sept. 11, 2001, killing all 64 aboard the hijacked plane and 125 people in the building.
Asked about the chances of capturing Osama bin Laden, whose al Qaeda network is blamed for the attacks on New York and Washington, Rumsfeld said he was certain he would be caught eventually. Karzai said bin Laden was on the run and could not stay hidden indefinitely.
"Has a fugitive run forever? No, at least not in my country," he said. "We will catch him one day, sooner or later."
Karzai, who is president by vote of a loya jirga, or grand council, under traditional Afghan practice, is running for the presidency in the September election against a number of challengers.
He said he was satisfied that the U.S. government has remained focused on its commitment to help Afghanistan establish a national government and to rebuild from years of war.
"We would not be having a specific request for more U.S. troops in Afghanistan," he said. "The United States is already busy in Afghanistan helping us in reconstruction and helping us fight terrorism and helping us secure our borders."
The United States in recent months has increased its force in Afghanistan, which now stands at about 20,000 troops.
Karzai seemed to hint at being weary of the heavy U.S. military presence in his country. As a helicopter flew overhead, prompting Karzai to interrupt his opening remarks, he said with a smile while pointing to the sky, "You see that too often in Afghanistan."
Meanwhile, in Karzai's homeland, Afghan troops killed four suspected Taliban militants and captured two more in a gunfight at a checkpoint in southern Afghanistan, a senior official said Tuesday.
The victims were in a pickup truck that failed to stop late Monday at the checkpoint in the Hazar Boosth area of Zabul province, 190 miles southwest of the capital, Kabul, Gov. Jan Mohammed Khan said.
A Chinese military plane left the Afghan capital on Monday with the bodies of 11 Chinese construction workers slain in their sleep in northern Afghanistan last week.
Afghan officials say they have arrested 10 people in connection with the attack, but it remains unclear whether Taliban-led insurgents battling U.S.-led forces in the south and east were responsible.
Nearly 500 people have died in violence across the country so far this year. Many are victims of the stubborn Taliban-led insurgency. Others have died in factional fighting linked to the country's booming drug trade.
A senior U.S. military official says the coalition stands "firmly behind the decision" to hold elections in Afghanistan in September — despite violence aimed at stopping them.
The military says plans being drawn up by foreign troops, the United Nations and Afghan leaders will encourage voter registration by increasing security. The U.N. says nearly a third of the Afghans eligible to vote are registered.
Across the border in Pakistan, authorities are trying to identify some of the scores of bodies of militants killed in a counterterrorism operation near the Afghan border to determine if any were key al Qaeda members, officials said Tuesday.
The in South Waziristan, about 210 miles west of the capital, Islamabad, ended Sunday after an assault on militant hideouts with artillery, helicopter gunships and jet fighters. At least 72 people, including 17 security forces, were killed.
Pakistan, a key ally of the United States in its war on terror, has launched a series of military operations in South Waziristan, where hundreds of foreign al Qaeda-linked militants are believed to be hiding — along with members of Afghanistan's former ruling Taliban regime.
Pakistan has deployed about 70,000 troops in its tribal regions to prevent Taliban and al Qaeda rebels from sneaking into Pakistan from Afghanistan.
Army spokesman Maj. Gen. Shaukat Sultan told The Associated Press it wasn't known if any key al Qaeda members was among the 55 dead militants. He gave no details about the nationalities of those killed, although he said earlier that some were foreigners.
Another security official said on the condition of anonymity that experts were trying to match dead terror suspects with photographs of "some al Qaeda men."
On Tuesday, Pakistani security forces shot dead a foreign man and wounded a woman and three children traveling with him after he opened fire at a checkpoint near the Afghan border, injuring a paramilitary soldier, an army spokesman said.
Elsewhere in the remote tribal region, three rockets landed near a Pakistani army checkpoint, but no one was hurt, residents said.
Meanwhile, the military said Monday that the U.S. military is changing procedures at its jails in Afghanistan following a review prompted by .