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 While President Obama has made no secret of his desire to withdraw American troops as rapidly as possible, the plans for a postwar American presence in Afghanistan have generally envisioned a residual force of thousands of troops to carry out counterterrorism operations and to help train and equip Afghan soldiers.

 In a conference call with reporters, the deputy national security adviser, Benjamin J. Rhodes, said that leaving no troops "would be an option that we would consider," adding that "the president does not view these negotiations as having a goal of keeping U.S. troops in Afghanistan."

 Military analysts have said it is difficult to conceive of how the United States might achieve even its limited post-2014 goals in Afghanistan without any kind of troop presence. That suggests the White House is staking out a negotiating position with both the Pentagon and with Mr. Karzai, as he and Mr. Obama begin to work out an agreement covering the post-2014 American role in Afghanistan.

 Discussing the administration's planning, Mr. Rhodes said the "core goal" of the United States was to "disrupt, dismantle and defeat Al Qaeda" and to "ensure that they can never return to Afghanistan."

 To that end, American military officers in Kabul and at the Pentagon have been developing plans for a commando force that could carry out raids against terrorist groups. Such a force would also need logistical support and arrangements for rapid medical evacuation, as well as helicopters that could whisk them to the battlefield and warplanes that could carry out airstrikes if they needed additional firepower.

 Another objective, Mr. Rhodes said, would be to "ensure that Afghan national security forces are trained and equipped."

According to a recent Pentagon report, only one of the Afghan National Army's 23 brigades is capable of operating without support from the United States and other NATO nations.  

 To help the Afghan military become more self-sufficient, the United States and its NATO allies have been discussing plans to advise Afghan troops after 2014. Gen. John R. Allen, the American commander in Kabul, initially outlined a series of options that ranged from 6,000 to 20,000 troops to carry out such missions.

 After the White House pressed for lower troop options, the Pentagon offered three plans that would leave 3,000, 6,000 and 9,000. Given the demanding nature of the mission in Afghanistan, the Pentagon officials have indicated the upper end of that limit is more realistic.

 Douglas E. Lute, the senior White House aide on Afghanistan, suggested that the requirement for troops could be low if the United States made progress against Al Qaeda over the next two years and the Afghan military improved.

 "The ranges are completely derivative from different assumptions about the variables," Mr. Lute said. "And that process with John Allen continues even as recently as today."

 Anthony H. Cordesman, a prominent military analyst at the Center for Strategic and International Studies, said in a recent report that the administration had disclosed so little about its plans for a military or civilian transition in Afghanistan that the debate over troop numbers was not meaningful.

"This lack of public and transparent plans and reporting makes it impossible to determine whether there is a real transition plan or a disguised exit strategy," he wrote.

 Mr. Karzai will meet Mr. Obama and Secretary of State Hillary Rodham Clinton at the White House on Friday. On Thursday, he will confer at the Pentagon with Secretary of Defense Leon E. Panetta. He is also scheduled to speak at Georgetown University on Afghanistan's future.