With President Vladimir Putin intensifying operations, a senior US defense official also warned that Russian strikes on civilians were mounting and that Moscow was seeking to recruit foreign fighters, notably Syrians, for the war.

The United States has already deployed 12,000 additional soldiers to Europe this year, but President Joe Biden has stressed that US troops will not engage in a conflict with Russian forces in Ukraine.

Over the weekend, Secretary of Defense Lloyd Austin ordered an extra "500 US military personnel to locations in Europe to augment existing forces," the defense official told reporters.

"These additional forces are going to be positioned to respond to the current security environment in light of Russia's renewed aggression against Ukraine, and to reinforce deterrence and defensive capabilities of NATO."

The Defense Department has assessed that of the Russian forces built up along the border -- estimated by Western nations at over 150,000 troops -- Putin "has committed nearly 100 percent of his combat power into Ukraine," the official said.

"He's got almost all of them in."

With Ukrainians trying to hold the assault at bay, Russia has engaged in more long-range attacks -- a mix of bombardments, rocket launches, artillery strikes and more than 625 missiles -- to make up for their lack of movement on the ground, the official said.

Bombardments have increased around the capital Kyiv, Kharkiv, Chernihiv in the north, and Mykolaiv and Mariupol in the south, and "we do assess that these strikes are hitting civilian targets, civil infrastructure, residential areas," he said.

It remained unclear whether the strikes on civilians were deliberate, but the official stressed that "it's happening at a greater rate and on a greater scale, and (is) all the more evidence of the reckless nature with which the Russians are propagating this invasion."

Meanwhile concern has grown that Odessa, the country's main port, is in Russia's sights.

Ukrainian President Volodymyr Zelensky warned on Sunday that Moscow was "preparing to bomb Odessa."

But the defense official said the Pentagon has "not seen any evidence of a movement on Odessa" yet.

"We believe the Russians want to take Odessa," and the Pentagon was not ruling out the potential for a Russian amphibious assault supported by ground troops, he said.