BAGRAM AIR BASE, Afghanistan — Vice President Cheney dismissed fears that Afghanistan could slide into a failed state, telling troops on yesterday that American and NATO allies will not allow resurgent extremists to bully their way back into power.

More than 8,000 people died in Afghanistan last year, making it the most violent year since 2001 when America invaded Afghanistan to oust the Taliban regime after the terrorist attacks of September 11, 2001. Taliban and Al Qaeda fighters have regrouped, especially in the south, and the job of coordinating aid and NATO troops from scores of nations has proved daunting.

“The Afghan people have no desire to be pulled back into the dark ages,” Mr. Cheney said at Bagram Air Base during an unannounced trip to Afghanistan. “They’re trusting America to stand by them in this fight, and that trust is being repaid every day. Having liberated this country, the United States and our coalition partners have no intention of allowing extremists to shoot their way back into power.” Mr. Cheney said NATO members need to step up military assistance for Afghanistan as it struggles to rebound from years of tyranny and war. That will be at the top of the agenda when leaders of the 26 nations in NATO hold a summit in Romania early next month.

NATO’s force is about 43,000 strong, but NATO commanders seek more combat troops for areas in southern Afghanistan where Taliban and Al Qaeda fighters are the most active.

All 26 NATO nations have soldiers in Afghanistan, but the refusal of European allies to send more combat troops is forcing an already stretched American military to fill the gap. America contributes one-third of the NATO force, and also has about 12,000 other American troops operating independently from NATO.

The Pentagon says that by late summer, there will be about 32,000 American troops in Afghanistan — up from about 28,000 now. The bulk of the increase reflects the 3,200 additional Marines Mr. Bush recently sent to Afghanistan.