Russian mercenaries with combat experience in Syria and Libya are gearing up to assume an increasingly active role in a phase of the war in Ukraine that Moscow now says is its top priority: fighting in the country’s east.

The number of mercenaries deployed to Ukraine from the Wagner Group, a private military force with ties to President Vladimir V. Putin of Russia, is expected to more than triple to at least 1,000 fighters from about 300 a month ago, just before the invasion, a United States official said on Friday. The official added that the mercenaries would focus on defeating Ukrainian forces in the country’s Donbas region, where Russia-backed separatists have been fighting a war since 2014, and elsewhere in eastern Ukraine.

Dispatching trusted Russian mercenaries to help with a pivotal part of the Russian invasion underscores the Kremlin’s efforts to regroup and refocus its flagging, monthlong military campaign that so far has failed to achieve Mr. Putin’s initial goals, U.S. and other Western officials said.