The mayor of the Ukrainian port city of Mariupol said Monday that more than 10,000 civilians have died in the Russian siege of his city, and that the death toll could surpass 20,000, with corpses that were “carpeted through the streets.”

Speaking by phone Monday to The Associated Press, Mayor Vadym Boychenko also said Russian forces brought mobile cremation equipment to the city to dispose of the bodies, and he accused Russian forces of refusing to allow humanitarian convoys into the city in an attempt to conceal the carnage.

Russian forces have taken many bodies to a huge shopping center where there are storage facilities and refrigerators, Boychenko said.

“Mobile crematoriums have arrived in the form of trucks: You open it, and there is a pipe inside and these bodies are burned,” he said.

The mayor’s comments emerged as Russia claimed that it destroyed several Ukrainian air-defense systems in what appeared to be a renewed push to gain air superiority and take out weapons Kyiv has described as crucial ahead of an expected broad new offensive in the east.

In one strike, Moscow said it hit four S-300 launchers near the central city of Dnipro that had been provided by a European country it did not name. Slovakia gave Ukraine just such a system last week but denied it had been destroyed. Russia previously reported two strikes on similar systems in other places.

The failure to win full control of Ukraine’s skies has hampered Moscow’s ability to provide air cover for troops on the ground, limiting their advances and likely exposing them to greater losses.

With their offensive in many parts of the country thwarted, Russian forces have relied increasingly on bombarding cities — a strategy that has left many urban areas flattened and killed thousands of people.

Ukrainian authorities accuse Russian forces of committing atrocities, including a massacre in the town of Bucha, outside Kyiv, airstrikes on hospitals and a missile attack that killed at least 57 people last week at a train station.

In Bucha on Monday, the work of exhuming bodies from a mass grave in a churchyard resumed.

Galyna Feoktistova waited for hours in the cold and rain in hopes of identifying her 50-year-old son, who was shot and killed more than a month ago, but eventually she went home for some warmth. “He’s still there,” her surviving son, Andriy, said.

In Mariupol, about 120,000 civilians are in dire need of food, water, warmth and communications, the mayor said.

Only those residents who have passed the Russian “filtration camps” are released from the city, Boychenko said. He said improvised prisons were organized for those who did not pass the “filtering,” while at least 33,000 were taken to Russia or to separatist territory in Ukraine.

Meanwhile, the U.N. children’s agency said that nearly two-thirds of all Ukrainian children have fled their homes in the six weeks since Russia’s invasion began, and the United Nations has verified that 142 children have been killed and 229 injured, though the actual numbers are likely much higher.

Elsewhere, Austrian Chancellor Karl Nehammer said he met Monday with Russian President Vladimir Putin in Moscow for talks that were “very direct, open and tough.”

In a statement released by his office, Nehammer said his primary message to Putin was “that this war needs to end, because in war both sides can only lose.” Nehammer said he also raised the issue of war crimes committed by the Russian military and said those responsible “will be held to account.”

READ: Russian shelling traps residents of Mariupol

Austria is a member of the European Union and has backed the 27-nation bloc’s sanctions against Russia, though it so far has opposed cutting off deliveries of Russian gas. The country is militarily neutral and is not a member of NATO.

In other developments, the head of the separatist rebel government in Donetsk said Ukrainian forces have lost control of the port area of Mariupol.

“Regarding the port of Mariupol, it is now under our control,” Denis Pushilin, president of the Donetsk People’s Republic, told Russian state television, according to Russian news agencies. The claim could not immediately be confirmed.

The mayor said fighting continues.

“It is difficult, but our heroic military holds on,” Boychenko said. “There are fights in the port. Yesterday, our heroic warriors knocked out several positions of equipment and, accordingly, rebuffed the infantry.

Russia has appointed a seasoned general to lead its renewed push in the eastern Donbas region, where Moscow-backed separatists have been battling Ukrainian forces since 2014 and have declared independent states. Both sides are digging in for what could be a devastating war of attrition.

Russian forces will likely try to encircle the Donbas region from the north and the south as well as the east, said retired British Gen. Richard Barrons, co-chair of the U.K.-based strategic consulting firm Universal Defence & Security Solutions.

The ground in that part of Ukraine is flatter, more open and less wooded — so the Ukrainian ambush tactics used around Kiev may be less successful, Barrons said.

“As to the outcome, it’s finely balanced right now,” Barrons said. If the Russians learned from their previous failures, concentrated more force, connected their air force to ground forces better and improved their logistics, “then they might start to overwhelm the Ukrainian positions eventually, although I still think it would be a battle of enormous attrition.”

Ukrainian President Volodymyr Zelenskyy pleaded for more Western aid, saying his forces need heavier firepower. In a video address to South Korean lawmakers on Monday, Zelenskyy specifically requested equipment that can shoot down Russian missiles.

But those armaments could increasingly come under attack as Russia looks to shift the balance in the 6-week-old war.

Russian Defense Ministry spokesman Maj. Gen. Igor Konashenkov said the military used cruise missiles to destroy the four launchers Sunday on the southern outskirts of Dnipro. He said the military also hit such systems in the Mykolaiv and Kharkiv regions.

The Russian claims could not be independently verified.

The Pentagon said it had seen no evidence to support Russia’s claims. A senior U.S. defense official said Russia did conduct an airstrike Sunday on the airport in Dnipro, destroying some equipment, but the official said the U.S. has seen no indication that an air-defense system was knocked out.

Lubica Janikova, spokeswoman for Slovakia’s prime minister, denied Monday that the S-300 system it sent Ukraine had been destroyed. She said any other claim is not true.

Questions remain about the ability of depleted and demoralized Russian forces to conquer much ground after their advance on Kyiv was repelled by determined Ukrainian defenders.

Britain’s Defense Ministry said Monday that Ukraine has already beaten back several assaults by Russian forces in the eastern Donetsk and Luhansk regions — which make up the Donbas — resulting in the destruction of Russian tanks, vehicles and artillery.

Western military analysts say Russia’s assault increasingly is focusing on an arc of territory stretching from Kharkiv, Ukraine’s second-largest city, in the north, to Kherson in the south.

A residential area in Kharkiv was struck by incoming fire on Monday afternoon. Associated Press journalists saw firefighters putting out the fire and checking for victims following the attack, and saw that at least five people were killed, including a child.

Oleh Synyehubov, the regional governor of Kharkiv, said earlier Monday that Russian shelling had killed 11 people over the last 24 hours.