The Americans have asked NATO to maintain its current force levels — regardless of the drawdown — to carry the bulk of the training mission going forward.

“I think it’s pretty presumptuous of the United States to draw down and expect the European countries to keep their current levels,” said Rachel Rizzo, an adjunct fellow in the Transatlantic Security Program at the Center for a New American Security. “NATO wouldn’t be in Afghanistan if it wasn’t for the United States.”

But Pentagon officials pushed back on the notion that the United States has asked NATO to handle training Afghan forces, despite the fact that if the American military cuts its forces in Afghanistan and focuses on counterterrorism missions, the training mission, by definition, will be left to the alliance unless it leaves the country.

“The U.S. has not asked NATO to take up the bulk of the training mission if there is a decision to reduce the U.S. force presence,” said Lt. Col. Thomas Campbell, a Pentagon spokesman. “Both NATO and the U.S. remain committed to the shared goal of ensuring Afghanistan never again becomes a safe haven for terrorists to threaten the U.S. and its allies.”

Some European officials say they believe the continued international presence in Afghanistan has helped curb the flow of migrants and refugees out of the country. But as the war stretches on, many politicians want to see the alliance reduce its commitment in the country.

“Clearly many European capitals wouldn’t mind reducing their presence or turning the page on NATO’s Afghanistan chapter,” said Bruno Lété, an expert on the alliance in the Brussels office of the German Marshall Fund of the United States.

If allies decide to cut more deeply, the continued training of the Afghan military will hang in the balance. The alliance, which immediately backed the United States’ invasion in 2001, has been a stalwart, but sometimes unreliable, part of the war effort. The United States has often pushed NATO to contribute more forces, and the allied countries have struggled at times to find enough people to serve in the training billets they have agreed to fill.