KYIV (REUTERS) - Russia on Sunday (July 31) invited United Nations and Red Cross experts to probe the deaths of dozens of Ukrainian prisoners held by Moscow-backed separatists, while Ukraine's president ordered the evacuation of residents in the eastern region of Donetsk.

President Volodymyr Zelensky said hundreds of thousands of people were still exposed to fierce fighting in the Donbas region, which contains Donetsk and Luhansk province.

"Many refuse to leave but it still needs to be done," Zelensky said in a televised address late on Saturday. "The more people leave the Donetsk region now, the fewer people the Russian army will have time to kill."

Ukraine and Russia have traded accusations over a missile strike or explosion early on Friday that appeared to have killed dozens of Ukrainian prisoners of war in the front-line town of Olenivka in eastern Donetsk.

Russia invited experts from the UN and Red Cross to probe the deaths "in the interests of conducting an objective investigation", the defence ministry said on Sunday.

The International Committee of the Red Cross (ICRC) has not yet received permission to visit the site of Friday’s attack that killed dozens of Ukrainian prisoners of war, it said on Sunday, condemning the incident at the Olenivka facility.

“Families must receive urgent news of and answers on what happened to their loved ones. The parties must do everything in their power, including through impartial investigations, to help determine the facts behind the attack,” it said in a statement.

Red Cross teams were ready to deploy to Olenivka and already had medical, forensic, and humanitarian teams in the vicinity, it said.

“It is imperative that the ICRC be granted immediate access to the Olenivka facility, and other places where the wounded and dead might have been transferred in order to carry out its humanitarian mission,” it said, pointing out that warring parties were obliged to let it visit POWs wherever they may be.

“However, it is not the role or mandate of the ICRC to carry out public investigations into alleged war crimes.”

The Russian defence ministry had published a list of 50 Ukrainian prisoners of war killed and 73 wounded in what it said was a Ukrainian military strike with a US-made High Mobility Artillery Rocket System (Himars).

Ukraine's armed forces denied responsibility, saying Russian artillery had targeted the prison to hide mistreatment there.

Foreign Minister Dmytro Kuleba said on Friday that Russia had committed a war crime and called for international condemnation.

Reuters journalists confirmed some of the deaths at the prison, but could not immediately verify the differing versions of events.

The UN had said it was prepared to send experts to investigate if it obtained consent from both parties. The International Committee of the Red Cross said it was seeking access and had offered to help evacuate the wounded.

Ukraine has accused Russia of atrocities against civilians and identified more than 10,000 possible war crimes. Russia denies targeting civilians and war crimes in the invasion it calls a "special operation".

Ukrainian counteroffensive

Ukrainian forces attacked the Russian Black Sea Fleet headquarters in the Russian-held Crimean port city of Sevastopol early on Sunday, Sevastopol Governor Mikhail Razvozhayev was quoted by Russian media as saying.

Five members of staff were wounded in the attack when what was presumed to be a drone flew into the courtyard at the headquarters, he said.

Ukrainian authorities said the southern cities of Mykolaiv and Nikopol had been hit by heavy Russian strikes overnight.

Two people were killed and three wounded when 12 missiles hit homes and educational facilities, Mykolaiv Mayor Oleksandr Senkevych told Ukrainian national television, describing the strikes as “probably the most powerful” on the city of the entire war.

Up to 50 Grad rockets hit residential areas in the city of Nikopol on Sunday morning, Dnipropetrovsk Governor Valentyn Reznichenko wrote on Telegram. One person was wounded.

Ukraine's military said on Saturday more than 100 Russian soldiers had been killed and seven tanks destroyed in the south on Friday, including the Kherson region that is the focus of Kyiv's counteroffensive in that part of the country and a key link in Moscow's supply lines.

Rail traffic to Kherson over the Dnipro River had been cut, the military's southern command said, potentially further isolating Russian forces west of the river from supplies in occupied Crimea and the east.

South of the town of Bakhmut, which Russia has cited as a prime target in Donetsk, the Ukrainian military said Russian forces had been "partially successful" in establishing control over the settlement of Semyhirya by storming it from three directions.

Defence and intelligence officials from Britain, which has been one of Ukraine's staunchest allies since Moscow invaded its neighbour on Feb 24, portrayed Russian forces as struggling to maintain momentum.

Ukraine has used Western-supplied long-range missile systems to badly damage three bridges across the Dnipro in recent weeks, cutting off Kherson city and - in the assessment of British defence officials - leaving Russia's 49th Army highly vulnerable on the river's west bank.

Reuters could not independently verify the battlefield reports.

Officials from the Russian-appointed administration running the Kherson region earlier this week rejected Western and Ukrainian assessments of the situation.

On Friday the British ministry described the Russian government as "growing desperate", having lost tens of thousands of soldiers in the war.

British MI6 foreign intelligence agency chief Richard Moore added on Twitter that Russia is "running out of steam".