How Far Would Biden Go to Defend Ukraine Against Russia?

Russia has not explicitly threatened to invade Ukraine, but it has complained of alleged provocations from the Ukrainian side of their shared border. Mr. Putin has supported a pro-Russian separatist insurgency in the former Soviet republic’s east since 2014, when a popular revolution ousted Ukraine’s Putin-backed president. Russia annexed Ukraine’s Crimean Peninsula soon afterward.

In a sign of the increasing tensions, the chairman of the Joint Chiefs of Staff, Gen. Mark A. Milley, spoke by phone on Tuesday with his Russian counterpart, Gen. Valery Gerasimov. The Pentagon said in a statement that the call was meant to “ensure risk reduction and operational de-confliction.”

Ukraine’s president, Volodymyr Zelensky, has said that the United States is providing information and data to Kyiv about the Russian force buildup. Western officials have confirmed that NATO allies are stepping up intelligence sharing with Ukraine, in hopes that a better understanding of the rising threat will help Kyiv better prepare and better deter Moscow.

Even in worst-case scenarios, most analysts say, Kyiv should not expect the U.S. military to come to its rescue.

“The Russians know full well, because they’ve been invading Ukraine for seven years now, that we’re not going to send in the 82nd Airborne,” said Samuel Charap, a former State Department official now with the RAND Corporation. “And I think they have likely priced in everything short of that, in the sense that they are willing to pay the price.”

“That’s what makes this hard,” he added. “There’s no easy way out of this.”

American officials said they did not believe that Mr. Putin had yet decided whether to take military action against Ukraine. While the threat is being taken seriously, officials said, the United States and its allies have time to try to prepare Kyiv and convince Moscow that such a move would be a terrible mistake.

Whatever Mr. Putin’s thinking, his troop buildup is likely to test the willingness of the United States, NATO and Europe to act.