KABUL, Afghanistan (CNN) -- President Bush made a surprise visit to Afghanistan on Wednesday, his first to the country where U.S. forces ousted the Taliban following the September 11, 2001, terrorist attacks.

Bush met with Afghan President Hamid Karzai during a five-hour unannounced stopover en route to India and Pakistan.

A group of low-flying helicopters carried Bush and his entourage from Bagram Air Base, the headquarters for U.S. troops, to the capital of Kabul, where he was received by Karzai.

After meeting with Karzai at the presidential palace, Bush told reporters he remained confident al Qaeda leader Osama bin Laden "will be brought to justice" despite a so-far futile hunt. "We're making progress of dismantling al Qaeda," Bush said as he stood beside Karzai outside the palace.

"Slowly but surely we're bringing the people to justice and the world is better for it." Karzai hailed Bush as "our great friend, our great supporter, a man who helped us liberate."

Bush said bin Laden, the mastermind of the September 11 terrorist attacks, eventually will be caught.

"It's not a matter of if they're captured and brought to justice, it's when they're brought to justice," Bush said.

Bush also congratulated the Afghan people, who voted in parliamentary elections in September. "People all over the world are watching the experience here in Afghanistan," he said.

"I hope that the people of Afghanistan understand that as democracy takes hold, you're inspiring others."

Bush presided over a ceremonial ribbon-cutting for the U.S. Embassy and spoke to troops at Bagram before continuing to India and Pakistan.

This was Bush's first trip to Afghanistan, where an October 2001 U.S. invasion eventually toppled the Taliban regime that had harbored bin Laden and allowed terrorist training camps on its soil. On Tuesday, the director of the U.S. Defense Intelligence Agency said that while Afghanistan had successful national and provincial elections in 2005, the Taliban "remains capable and resilient."

"In 2005, the Taliban and other anti-coalition movement groups increased attacks by 20 percent," Lt. Gen. Michael Maples told the Senate Armed Services Committee.

"We judge that the insurgency appears emboldened by perceived tactical successes and will be active this spring."