President Biden is considering deploying several thousand U.S. troops, as well as warships and aircraft, to NATO allies in the Baltics and Eastern Europe, an expansion of American military involvement amid mounting fears of a Russian incursion into Ukraine, according to administration officials.

The move would signal a major pivot for the Biden administration, which up until recently was taking a restrained stance on Ukraine, out of fear of provoking Russia into invading. But as President Vladimir V. Putin has ramped up his threatening actions toward Ukraine, and talks between American and Russian officials have failed to discourage him, the administration is now moving away from its do-not-provoke strategy.

In a meeting on Saturday at Camp David, the presidential retreat in Maryland, senior Pentagon officials presented Mr. Biden with several options that would shift American military assets much closer to Mr. Putin’s doorstep, the administration officials said. The options include sending 1,000 to 5,000 troops to Eastern European countries, with the potential to increase that number tenfold if things deteriorate.

The officials spoke on the condition of anonymity because they were not authorized to talk publicly about internal deliberations.

Mr. Biden is expected to make a decision as early as this week, they said. He is weighing the buildup as Russia has escalated its menacing posture against Ukraine, including massing more than 100,000 troops and weaponry on the border and stationing Russian forces in Belarus. On Saturday, Britain accused Moscow of developing plans to install a pro-Russian leader in Ukraine.

“Even as we’re engaged in diplomacy, we are very much focused on building up defense, building up deterrence,” Secretary of State Antony J. Blinken said in an interview that aired Sunday on CBS’s “Face the Nation.” “NATO itself will continue to be reinforced in a significant way if Russia commits renewed acts of aggression. All of that is on the table.”

So far, none of the military options being considered include deploying additional American troops to Ukraine itself, and Mr. Biden has made clear that he is loath to enter another conflict following America’s painful exit from Afghanistan last summer after 20 years.

But after years of tiptoeing around the question of how much military support to provide to Ukraine, for fear of provoking Russia, Biden officials have recently warned that the United States could throw its weight behind a Ukrainian insurgency should Mr. Putin invade Ukraine.

And the deployment of thousands of additional American troops to NATO’s eastern flank, which includes Estonia, Latvia and Lithuania, Biden administration officials said, is exactly the scenario that Mr. Putin has wanted to avoid, as he has seen the western military alliance creep closer and closer to Russia’s own border.

The discussions came as the State Department ordered all family members of U.S. embassy personnel in Kyiv to leave Ukraine, citing the threat of Russian military action, and authorized some embassy employees to depart as well, according to senior State Department officials who briefed reporters on Sunday. The officials, who also spoke on the condition of anonymity because they were not authorized to comment, declined to say how many embassy personnel and family members were in the country. Thinning out staff at American embassies is a common precaution when conflicts or other crises arise that could put American diplomats in harm’s way.

In his news conference last week, Mr. Biden said he had cautioned Mr. Putin that a Russian invasion of Ukraine would prompt Washington to send more troops to the region.

“We’re going to actually increase troop presence in Poland, in Romania, et cetera, if in fact he moves,” Mr. Biden said. “They are part of NATO.”

During a phone call this month, Defense Secretary Lloyd J. Austin III warned his Russian counterpart, Sergey Shoygu, that a Russian incursion into Ukraine would most likely result in the exact troop buildup that Mr. Biden is now considering.