The speaker of Russia's lower house of parliament says many fighters of the Wagner mercenary group have agreed to sign contracts with the country's defense ministry.

The ministry had urged the fighters to sign contracts by Saturday.

The chairman of the State Duma, Vyacheslav Volodin, wrote in a social media post on Sunday that, as far as he knew, many of them agreed.

This comes after Belarusian President Alexander Lukashenko reportedly offered Wagner fighters the use of camps in his country.

Meanwhile, Ukrainian and Russian forces are apparently locked in fierce fighting once again over control of the city of Bakhmut in the eastern region of Donetsk.

Ukrainian deputy defense minister Hanna Maliar said on social media on Sunday that Ukrainian forces had partial success in advancing in the southern part of Bakhmut.

But she said Russia transferred troops to the north of the city and fighting continued there.

In May, the Russian side claimed that it had taken full control of Bakhmut.

The Ukrainian presidential office says President Volodymyr Zelenskyy visited the southern region of Odesa on Sunday to mark the country's Navy Day.

He was reportedly briefed by the naval commander on operations in the Black Sea and on the Russian military's missile attack capabilities from the sea.

Zelenskyy said in a speech he is confident that Ukraine will get back everything that is temporarily controlled by Russia.