President Biden has yet to be presented with the proposal. But if he approves it, troops would be deployed only for the defense and security of the embassy, which lies within range of Russian missiles, U.S. officials said. Their presence inside Ukraine would mark an escalation from Mr. Biden’s initial pledge that no American troops will be sent into the country.

The administration seeks to balance concerns within the State Department that a robust, conspicuous security posture at the embassy could provoke Russian President Vladimir Putin with the need to deter a potential attack on American personnel—and have sufficient forces to extract them if fighting breaks out again in Kyiv. Russia continues to target the Ukrainian capital with occasional airstrikes or shelling even as the city has begun to return to normal.

For now, the State Department will furnish its own security, from a corps of guards in the Diplomatic Security Service, for the embassy in Kyiv.