Moscow says more than 900 Ukrainian fighters from the Mariupol steelworks have been taken to a former prison colony, in a Russian-controlled part of Donetsk.
Ukraine hasn't publicly commented on their fate. A pro-Russian separatist leader says more than 1,000 soldiers are still trapped in the plant.
Ukraine has ordered its garrison in Mariupol to stand down, but the ultimate outcome of Europe's bloodiest battle for decades remains unresolved.
Top commanders of Ukrainian fighters who had made their last stand at the Azovstal steelworks in the port city are still inside the plant, according to the leader of pro-Russian separatists in control of the area, Denis Pushilin, quoted by local news agency DNA on Wednesday.
Ukrainian officials have declined to comment publicly on the fate of the fighters.
"The state is making utmost efforts to carry out the rescue of our service personnel," military spokesman Oleksandr Motuzaynik told a news conference. "Any information to the public could endanger that process."
Ukraine confirmed the surrender of more than 250 fighters on Tuesday but did not say how many more were inside.
The international Red Cross says it has registered “hundreds” of Ukrainian prisoners of war who left the Azovstal steel plant in Mariupol, reported AP.
The Red Cross said in a statement that the operation continued Wednesday and was still ongoing Thursday. The International Committee of the Red Cross said it is not transporting them to the places where they are held, which is in separatist-controlled territory in eastern Ukraine.
“The registration process that the ICRC facilitated involves the individual filling out a form with personal details like name, date of birth and closest relative,” it said. “This information allows the ICRC to track those who have been captured and help them keep in touch with their families.”
On 16 May, the Ukrainian General staff announced that the Mariupol garrison had “fulfilled its combat mission” and that evacuations from the Azovstal steel factory had begun. The military said that 264 service members, 53 of them "seriously injured", had been taken by bus to areas controlled by Russian forces.
A social media post was released by Azov Regiment commander Denis Prokopenko stating: "In order to save lives, the entire Mariupol garrison is implementing the approved decision of the Supreme Military Command and hopes for the support of the Ukrainian people."
This statement follows Russia's decision to evacuate wounded Ukrainian soldiers from the Azovstal plant and for them to be taken to the DPR-controlled town of Novoazovsk for treatment.
Ukrainian Deputy Defence Minister Hanna Malyar said: "Thanks to the defenders of Mariupol, Ukraine gained critically important time to form reserves and regroup forces and receive help from partners. And they fulfilled all their tasks. But it is impossible to unblock Azovstal by military means."
Russia press secretary Dmitry Peskov said Russian President Vladimir Putin had guaranteed that the fighters who surrendered would be treated "in accordance with international standards" while Ukrainian President Volodymyr Zelenskyy said in an address that "the work of bringing the boys home continues, and this work needs delicacy – and time".
Some prominent Russian lawmakers called on the government to deny prisoner exchanges for members of the Azov Regiment.
Russia had justified its invasion of Ukraine by specifically calling it a "special military operation" designed to "de-nazify" the country.
