Ukrainian President Volodymyr Zelenskyy has encouraged his frontline troops in the country's east, saying Ukraine's future hinges on battles there.

Fierce fighting continues between Russian and Ukrainian forces for control of Ukraine's eastern stronghold of Bakhmut in the Donetsk region.

A US think tank, the Institute for the Study of War, said on Monday that Russian forces continued making advances northwest and southwest of Bakhmut, but have not succeeded in surrounding the city.

President Zelenskyy said in a video message released on Monday, "It is very tough in the east, very painful."

He said the country's future is being decided in Bakhmut, Vuhledar and elsewhere, and that it is a fight for the future of all Ukrainians.

Meanwhile, the British defense ministry on Tuesday expressed its view that Russian forces are also facing difficulties.

The ministry said that Russian artillery ammunition shortages have likely worsened in the past few weeks. It added that Russia has almost certainly already resorted to issuing old munitions stocks that had previously been categorized as unfit for use.