The Ukrainians are "in places and at times going on an offensive," particularly in the south of the country, US Defense Department spokesman John Kirby told CNN.

"They are going after Russians and pushing them out of places where the Russians have been in the past," he said, particularly in Mykolaiv.

"We have seen this now increase over the last few days."

Kirby said he could not confirm reports from Ukrainian officials that they had retaken at least one town and expect to take more in coming days.

But it would be "consistent with the kind of fighting and the kinds of capabilities we have seen the Ukrainians use," he said.

As for the Russians, he echoed Western analysts who have said the invading forces have become bogged down.

"They are running out of fuel. They're running out of food. They are not integrating their operations in a joint manner the way you would think a modern military would," Kirby said.

He said Russian commanders "aren't necessarily talking to one another," and that there were communication problems between air and ground forces.

In some cases the Russian fighters have had to resort to using cellphones to communicate with each other.

The Russians are "frustrated" and "stalled," he said, citing the fact Moscow's forces have failed to take control of population centers beyond two areas around Kherson and Melitopol in the south.

"They are slowed. And some of that... is due to their own ineptitude."

Separately a senior Pentagon official, speaking on grounds of anonymity, said Tuesday that the Ukrainian army had launched a counterattack on Russian forces in Izyum, a small city southeast of Kharkiv.

Izyum is on a key route to the Donbas region that would potentially allow Russian forces in the northeast and southeast to link up.

"What we're seeing today is some significant fighting there by the Ukrainians, and an effort to take it back," the official said of Izyum.

The official said that due to losses and other problems the Russia force inside Ukraine is now below 90 percent of its available combat power.

In addition to problems getting food and fuel to its units, the Russian military has had to take soldiers out of the fight due to frostbite, the official said.

"They lack the appropriate cold weather gear for the environment that they are in," the official said.