Russian missiles have struck cities across Ukraine, including the capital Kyiv, the Black Sea port of Odesa and the second city of Kharkiv, while Ukrainian defenders repelled fierce assaults on the beleaguered town of Bakhmut.

The missiles hit a wide arc of targets, including cities stretching from Zhytomyr, Vynnytsia and Rivne in the west to Dnipro and Poltava in central Ukraine, officials said on Thursday.

There were no immediate reports of any casualties.

Kyiv mayor Vitali Klitschko said explosions were registered in the southwestern part of the town and rescue services were on their way. Some residents reported power cuts.

The governor of Odesa region, Maksym Marchenko, said on Telegram that a mass missile attack had hit an energy facility in the port city, cutting power. Residential areas had also been hit.

Kharkiv region Governor Oleh Synehubov said the city and region had been hit by 15 strikes, with targets including infrastructure. Other strikes were reported in the central city of Dnipro and regions throughout the country.

Late on Wednesday, Ukraine's military said its forces had managed to push back intense Russian attacks on the eastern mining town of Bakhmut, despite a Russian claim of control of its eastern half.

As one of the bloodiest battles of the year-long war ground on in the town's ruins, Ukrainian defenders - who last week appeared to be preparing for a tactical retreat - remained defiant.

"The enemy continued its attacks and has shown no sign of a letup in storming the city of Bakhmut," the General Staff of the Ukrainian armed forces said on Facebook. "Our defenders repelled attacks on Bakhmut and on surrounding communities."

Ukrainian military and political leaders now speak of hanging on to positions and inflicting as many casualties as possible on the Russians to grind down their fighting capability.

President Volodymyr Zelenskiy said in a video address late on Wednesday the battle for Bakhmut and the surrounding Donbas region was "our first priority".

In a separate interview with CNN, he said: "We think that in the Donbas direction Russia has started its offensive. This is the offensive. This is what it looks like: a slow aggression, because they don't have enough strength and forces."

Yevgeny Prigozhin, head of the Russian mercenary group Wagner, said his fighters had captured the eastern part of Bakhmut. If true, Russian forces would control nearly half the city in a costly pursuit of their first big victory in several months.

"Everything east of the Bakhmutka River is completely under the control of Wagner," Prigozhin said on the Telegram messaging app.

The river bisects Bakhmut, on the edge of Ukraine's Donetsk province that is already largely under Russian occupation. The town centre is on the west side of the river.

Prigozhin has issued premature success claims before. Reuters was unable to verify the situation on the ground.

Ukrainian military analyst Oleh Zhdanov said that in addition to the Zabakhmutka district on the eastern outskirts of Bakhmut, the Russians had captured Ilyinivka district on the north side.

"The situation is critical," he said in a video commentary, adding that Russian forces had also made gains near Avdiivka to the south of Bakhmut as well as to the north around Svatovo.

Russia was throwing more troops into the battle, NATO Secretary-General Jens Stoltenberg said before a meeting of European Union defence ministers in Stockholm.

"They have suffered big losses, but at the same time we cannot rule out that Bakhmut may eventually fall in the coming days," Stoltenberg said.

European Union defence ministers agreed to speed up the supply of artillery rounds and buy more shells to help Ukraine's military, which is burning through shells faster than its allies can manufacture them.

Russia has said it has annexed nearly 20 per cent of Ukraine's territory and says taking Bakhmut would be a step towards seizing the whole of the industrial Donbas region on its border.