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And the country's rights ombudswoman accused Russian troops in the region of torture and executions.
Reuters reports it has confirmed widespread destruction in Mariupol but could not verify the crimes or the estimate of those killed in the strategic city.
"Mariupol has been destroyed, there are tens of thousands of dead, but even despite this, the Russians are not stopping their offensive," President Volodymyr Zelenskyy said in a video address to South Korean legislators.
If confirmed, it would be by far the largest number of dead so far reported in one place in Ukraine, where cities, towns and villages have come under relentless bombardment and bodies, including those of civilians, have been seen in the streets.
The head of the Russia-backed self-proclaimed Donetsk People's Republic, Denis Pushilin, told RIA news agency on Monday that more than 5,000 people may have been killed in Mariupol.
Mr Pushilin said Ukrainian forces were responsible.
The numbers of people leaving the city had fallen because Russian forces had slowed pre-departure checks, Petro Andryushchenko, an aide to the mayor of Mariupol, said on Monday on Telegram.
About 10,000 people were waiting to be screened by Russian forces, he said. Russia does not allow military personnel to leave with civilian evacuees.
There was no immediate comment from Moscow, which has previously blamed Ukraine for blocking departures.
Quoting figures from Mariupol's city administration, Ukraine's human rights ombudswoman Lyudmyla Denisova said 33,000 residents had been deported to Russia or territories held by Moscow-backed separatists in eastern Ukraine.
Russia said on Sunday it had "evacuated" 723,000 people from Ukraine since the start of what it called its "special operation." Moscow denies attacking civilians.
"Witnesses report that Russian national guard troops and Kadyrovite [Chechen] units are making illegal arrests, torturing detainees and executing them for any pro-Ukrainian stance," in Mariupol, Ms Denisova said in a post on Telegram.
Ukrainian Interior Ministry adviser Anton Geraschenko said on Monday that Ukrainian "deportees" were kept in guarded sanatoriums and holiday camps.
"These people are not allowed to move around freely or to have free access to communication platforms in order to contact their relatives in Ukraine," Mr Geraschenko said.
Ukraine's Deputy Prime Minister, Iryna Vereshchuk, told Reuters that the number of checkpoints along the Russian-controlled corridor between Mariupol to the Ukrainian city of Zaporizhzhia had grown from three to 15.
Mariupol was among nine humanitarian corridors agreed to with Russia on Monday to move people from besieged eastern regions, but its corridor was for private cars only, Ms Vereshchuk said on Telegram.
It was not possible to agree on the provision of buses, she said.
Ukraine says Russian forces are massing for a new offensive on eastern areas, including Mariupol, where people have been without water, food and energy supplies for weeks.