WASHINGTON — The Pentagon has proposed to President Obama that 10,000 American troops remain in Afghanistan when the international combat mission there ends after this year, or none at all, senior government officials said Tuesday.

That figure, debated in recent days within the White House, is the midpoint of a range of 8,000 to 12,000 troops — most of them Americans — that has been contemplated for months as the United States and its NATO allies planned for the long mission’s end. Anything less than that, the officials said, would be too few to be able to protect the reduced retinue of diplomats, military and intelligence officials that remain in Afghanistan.

“The proposal is 10,000 or basically nothing, a pullout,” said one official, who has been briefed on the plan but spoke on the condition of anonymity about internal administration deliberations.

Both the intelligence agencies and the State Department, who would have personnel remaining in Afghanistan after 2014, back the Defense Department’s proposal, the officials said. But it has met resistance among some officials in the White House National Security Council, including Vice President Joseph R. Biden Jr., who question why the choice has to be 10,000 troops or zero, and nothing in between.