Russian forces carried out continuous attacks on the eastern Ukrainian city of Bakhmut in their quest for a breakthrough in the year-long war, and one U.S. official predicted few short-term territorial gains for Russia.

Ukrainian aircraft launched three strikes on areas of concentration of Russian forces, according to a statement by the General Staff of the Ukrainian Armed Forces on Tuesday night.

Bakhmut had a pre-war population of around 70,000 but has been ruined during months of fighting as a focal point of Russian assaults and determined Ukrainian defence.

"The most difficult part, as before, is Bakhmut and the fighting that is essential for the city's defence," Ukrainian President Volodymyr Zelenskiy said in his nightly video address.

"Russia in general takes no account of people and sends them in constant waves against our positions, the intensity of the fighting is only increasing," Zelenskiy said.

A Russian takeover of Bakhmut would open the way to seizing the last remaining urban centres in the industrial Donetsk province.

While most of the Russian attacks were focused on Bakhmut and other towns and villages in Donetsk, the military statement said Russian forces shelled more than 20 settlements in northern regions near the Russian border: Chernihiv, Sumy and Kharkiv.

Reuters was not able to verify battlefield reports.

Russia's state-run RIA news agency released a video clip it said showed Russian Su-25 fighter jets roaring over Bakhmut.