Ukrainian President Volodymyr Zelenskiy and his defence minister said they held a series of calls with Kyiv's allies on Sunday to discuss the "weakness" of Russia's President Vladimir Putin and Ukraine's next counteroffensive steps.

The phone calls took place after an extraordinary failed mutiny by the head of Russia's Wagner mercenary group, Yevgeny Prigozhin, that raised questions about Putin's grip on power as Ukraine presses a counteroffensive in its south and east.

"We discussed the course of hostilities and the processes taking place in Russia. The world must put pressure on Russia until international order is restored," Zelenskiy said after a phone call with U.S. President Joe Biden.

According to the White House readout, the two leaders "discussed Ukraine's ongoing counteroffensive, and President Biden reaffirmed unwavering U.S. support."

Oleksii Reznikov, Ukraine's defence minister, said he and U.S. Defence Secretary Lloyd Austin discussed Ukraine's counteroffensive and next steps to strengthen the forces.

"Things are moving in the right direction," Reznikov wrote on Twitter.

While Ukraine's officials said the Russia chaos works to Kyiv's advantage, it yet remains to be seen whether Zelenskiy and his army can capitalise on the Moscow disorder to reclaim territories now occupied by Russia.

Serhiy Cherevatyi, spokesperson for Ukraine's eastern military command, said on Sunday Kyiv's army advanced 600 metres (2,000 ft) to 1,000 metres over the previous day near Bakhmut, a city taken by Wagner forces in May after months of fighting.

But the gains have been incremental so far, with Zelenskiy saying recently the counteroffensive has been "slower than desired."

On Sunday, Zelenskiy said he and Biden had discussed expanding defence cooperation with an emphasis on long-range weapons, coordination ahead of the NATO summit in Vilnius next month and preparations for a "Global Peace Summit" he has promoted.

"Yesterday's events exposed the weakness of Putin's regime," Zelenskiy was quoted in the statement.

Separately, Zelenskiy said he had told Canadian Prime Minister Justin Trudeau in a call about the "threatening situation" at Ukraine's vast, Russian-occupied Zaporizhzhia nuclear power plant.

Zelenskiy warned earlier this week that Russia was considering carrying out an act of "terrorism" involving the release of radiation at the plant, an allegation denied by Russia.

"Ukraine's partners must demonstrate a principled response, in particular at the NATO Summit in Vilnius," he said.

The Ukrainian leader made similar comments in a statement announcing a phone call with Polish President Andrzej Duda.