The Taliban say they will step up their fight in Afghanistan, after pledges by the US and its allies to send large reinforcements to the country.
A Taliban spokesman said such moves would "provoke stronger resistance".
US President Barack Obama, announcing a long-awaited strategy on Tuesday, said another 30,000 American troops would be deployed quickly in Afghanistan.
Nato's secretary general said non-US members would contribute at least 5,000 extra troops next year.
"Obama will witness lots of coffins heading to America from Afghanistan," Taliban spokesman Qari Yousuf Ahamdi told AFP news agency.
"Their hope to control Afghanistan by military means will not become reality."
Mr Obama reached his deployment decision after more than three months of deliberations and 10 top-level meetings with advisers.
Stressing that the US was in Afghanistan because of the 9/11 attacks on America by al-Qaeda militants, the president said their Taliban allies had "begun to take control over swathes of Afghanistan" while committing "devastating acts of terrorism" against Pakistan.
US forces, he said, lacked "the full support they need to effectively train and partner with Afghan security forces and better secure the population".
"I have determined that it is in our vital national interest to send an additional 30,000 US troops to Afghanistan," he told the cadets.
"After 18 months, our troops will begin to come home."
The mission in Afghanistan, Mr Obama said, was to defeat al-Qaeda, reverse the Taliban's momentum and deny them the ability to overthrow the government.
Gen Stanley McChrystal, the US commander in Afghanistan, who had asked for 40,000 extra troops, welcomed the speech, saying he had been given "a clear military mission" and the necessary resources.
The reinforcements will take the total number of US troops in Afghanistan to more than 100,000.
Some 32,000 other foreign troops are serving there. Nato Secretary General Anders Fogh Rasmussen urged members to do more.
He told reporters on Wednesday that 5,000 extra troops would be sent in 2010, and "probably" a few thousand in addition.
"This is our fight together," he said. "We must finish it together."
The Afghan government said it supported the new US strategy.
Foreign Minister Rangin Dadfar Spanta said that with international help, Afghanistan's armed forces would be able to start taking responsibility for security in 18 months.
