And it remains unclear whether several thousand NATO and other foreign troops are really the equal of a similarly sized American force in terms of military capacity. Some countries may continue to restrict how their forces may be employed. In addition, a force that is cobbled together from too many nations  a few hundred here and a thousand there  might not have the unit cohesion of an American force, military analysts said.

Washington has not yet made formal troop requests to allies, but there have been diplomatic and other conversations seeking commitments in principle, carried out by senior American officials; the NATO secretary general, Anders Fogh Rasmussen; and Prime Minister Gordon Brown of Britain.

Image French soldiers returning to an outpost after a recent operation east of Kabul. France is standing firm on its refusal to consider sending more of its forces to Afghanistan. Credit... Jerome Delay/Associated Press

Mr. Obama’s aides have signaled that he intends to commit close to 30,000 additional American troops, on top of the 68,000 already there.

The president is likely to ask NATO allies to fill the gap between whatever new American troop contribution he announces and the approximately 40,000 that the NATO commander in Afghanistan, Gen. Stanley A. McChrystal, favors to carry out his proposed counterinsurgency strategy, according to administration officials. The officials spoke on the condition of anonymity because the policy had not been formally announced.

After Mr. Obama gives his speech and Mr. Rasmussen delivers a statement of support, NATO foreign ministers are to meet in Brussels next Thursday and Friday to discuss Afghanistan. But troop commitments are not likely to be discussed in detail before a so-called force-generation conference on Dec. 7, also in Brussels, American and allied officials said.

Informal commitments of several thousand additional allied troops have already been made, but they include some of the 10,000 more European troops that were sent to Afghanistan by governments last year, as well as troops sent for the recent presidential election, NATO officials said.