There was no count of civilian casualties, he told CNN on Friday.
He said 19,000 to 20,000 Russian soldiers had been killed in the war, now in its eighth week. Moscow said last month that 1351 Russian soldiers had been killed and 3825 wounded.
Reuters could not independently verify either side's numbers.
Fighting was intense in Mariupol as Ukraine said it was trying to break Russia's siege of the southeastern port city. Home to 400,000 people before Russia's invasion, Mariupol has been reduced to rubble. Thousands of civilians have died and tens of thousands remain trapped.
Russia said it struck what it described as a factory on the outskirts of the capital Kyiv that made and repaired anti-ship missiles, after the sinking on Thursday of the Moskva, the flagship of Moscow's Black Sea fleet.
Ukraine said one of its missiles had caused the Moskva to sink, a powerful symbol of its resistance to a better-armed foe. Moscow said the ship sank while being towed in stormy seas after a fire caused by an explosion of ammunition and that more than 500 sailors were evacuated.
The United States believes the Moskva was hit by two Ukrainian missiles and that there were Russian casualties, although numbers were unclear, a senior US official said.
None of the assessments could be independently verified.
Zelenskiy said the military situation in the south and east was "still very difficult," while praising the work of his armed forces.
"The successes of our military on the battlefield are really significant, historically significant. But they are still not enough to clean our land of the occupiers. We will beat them some more," he said in a late-night video address, calling again for allies to send heavier weapons and for an international embargo on Russian oil.
Zelenskiy has appealed to US President Joe Biden for the United States to designate Russia a "state sponsor of terrorism," joining North Korea, Cuba, Iran and Syria, the Washington Post reported, citing people familiar with their conversation.
A White House spokesman responded by saying, "We will continue to consider all options to increase the pressure on Putin."
If Moscow captures Mariupol, it would be the first big city to fall.
Russia's defence ministry said it had captured the city's Illich steel works. The report could not be confirmed. Ukrainian defenders are mainly believed to be holding out in Azovstal, another huge steel works.
Moscow has used its naval power to blockade Ukrainian ports and threaten a potential amphibious landing along the coast. Without the Moskva, the largest warship sunk during conflict since Argentina's General Belgrano in the 1982 Falklands war, its ability to menace Ukraine from the sea could be crippled.
Russia initially described its aims in Ukraine as "a special military operation" to disarm its neighbour and defeat nationalists there.
After its invasion force was driven from the outskirts of Kyiv this month, Moscow has said its main war aim is to capture the Donbas, the eastern region partly held by Russian-backed separatists since 2014.
Kyiv and its Western allies say those are bogus justifications for an unprovoked war of aggression that has driven a quarter of Ukraine's 44 million people from their homes and led to the deaths of thousands.
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