LVIV, Ukraine — After helping a friend stanch the bleeding from a shrapnel wound on Tuesday morning during a renewed shelling in Mariupol, Anastasia Kushnir and her family decided it was time to take the opportunity to get out of the besieged coastal city, where they had been struggling to stay alive for the past three weeks.
“There was heavy shelling and aerial bombardment,’’ said Ms. Kushnir, who is 21. “But we made it out, fortunately.”
Ms. Kushnir and her family members made it as far as Urzuf, a small beachside town on the Sea of Azov 28 miles from Mariupol, a way station on their way further north and west, to safety. A drive that usually takes 30 minutes took five hours, as their car joined a convoy of thousands of others trying to leave after waiting weeks for a humanitarian corridor to open.
About 160 cars left on Monday, and an estimated 4,000 cars, or 20,000 people, left the city on Tuesday, city officials said. Ms. Kushnir said she saw cars broken down along the road: many had run out of gasoline, which she said was nearly impossible to find in the region.
But still, she said in an interview, she was relieved to be out of Mariupol and away from the constant shelling.
“Humanitarian corridors have been partially opened today,” said President Volodymyr Zelensky in a speech on Tuesday. “Little by little people are leaving the besieged city by private transport.” However, he lamented that “a convoy with humanitarian cargo for Mariupol remains blocked. For several days in a row.”
About 2,000 vehicles had managed to escape the city by Tuesday afternoon, and another 2,000 were packed to leave before nightfall, Pyotr Andryushchenko, an assistant to Mariupol’s mayor, told The New York Times in a phone interview.
Officials told civilians hoping to leave to “delete all messengers and photos from phones” in case Russian soldiers tried to search them for signs of support for Ukrainian forces.
Ms. Kushnir said she and her family had tried to leave before, but the locations where a convoy was being organized were being shelled. While they waited, she said, she and her family slept on the floor of a room with no electricity, no lights, no windows and no heating.
“There is not a single residential building left with windows in my neighborhood,” she said. After five days, they started to run out of food. Residents organized into groups, with men walking amid the shelling to find water, and women improvising outdoor cook stoves to make watery vegetable soups.
Temperatures dropped to as low as 16 degrees Fahrenheit, Ms. Kushnir said. “We had to drink tea constantly to keep warm,” she said, adding that some elderly people had died of cold and hunger.
As she left her city by car, she saw bodies lying in the street, which the authorities had not managed to collect or bury.
“People who died are not buried, they just lie where they died,” she said. “There is an enormous number of them.”
With some residents crushed in the rubble from the relentless Russian onslaught and others dying in freezing conditions with no heat, food or clean water, officials in the besieged coastal city of Mariupol are struggling to account for the number of dead and missing.
Officially, 2,400 civilians killed in the city have been identified, but Mr. Andryushchenko said he believed the toll was far higher.
“We have inaccurate data on civilians killed,” he said in an interview with Current Time, a Ukrainian radio station. He said the official figure represented a “small handful” of those killed and estimated that the actual total could be as high as 20,000.
A battleground since the first hours of the war, Mariupol is under an increasingly relentless assault that is taking an unspeakable toll. Ukrainian estimates for the number of civilians trapped in the city have ranged from 200,000 to 400,000, with the latest estimate being 300,000.
The region’s top official, Pavlo Kyrylenko, who until martial law was declared was its governor, announced that the Russians were also holding doctors and patients of the main intensive care hospital hostage. An estimated 400 people are inside.
“It is impossible to get out of the hospital,” Mr. Kyrylenko wrote on Telegram, quoting a message from one of the facility’s employees. “They shoot hard, we sit in the basement. Cars have not been able to drive to the hospital for two days. High-rise buildings are burning around.”
Battered by Russian shelling, the city has been overwhelmed by the wounded and dead. Videos shared on Telegram showed residents of the Cheryomushki neighborhood burying a body in a courtyard. Another video showed how local people had turned a post office building into a makeshift morgue, with “MORGUE” spray-painted in large Cyrillic letters on the outside of the ground floor of the building.
“Here, in this building of the New Post Office on Cheryomushki, they stack corpses, which in the future they themselves will bury,” a man can be heard saying in the video, which he posted to the Telegram channel Mariupol Now.
Russian forces have dropped more than 100 bombs within the city limits, according to a Telegram post by the Mariupol city council, destroying nearly all basic services, even as they battle Ukrainian forces on the outskirts of the metropolis.
The Kremlin has said that it is Ukrainian forces that are keeping people trapped in the city. The Ukrainian government says that repeated attempts at mass evacuation have failed as they came under attack by Russian forces.
The Ukrainian Army’s high command said on Tuesday that its forces had managed to repel the latest Russian attempt to move into the city, claiming to have destroyed two tanks, seven infantry fighting vehicles and one armored personnel carrier. “After the losses, the occupiers stopped the offensive and retreated,” the Ukrainian military said.
The Ukrainians noted that their forces had also suffered losses. It is nearly impossible to independently verify almost any information out of Mariupol, as nearly all lines of communication have been severed.
Mr. Andryushchenko, the adviser to the city government, declined to comment in his phone interview with The Times on whether he and the mayor would be evacuating from the city. The mayor’s security would likely be of concern: Russian forces kidnapped the mayor of nearby Melitopol and installed a replacement.
“We sincerely hope for the safety of our mayor and that our defenders will help ensure it,” Mr. Andryushchenko said. “We know for sure that he will not accept the Russian occupation under any circumstances, will not cooperate with the occupiers and will not recognize any occupation authority.”
But he was also at a loss for words thinking about the city’s future. He has estimated that 80 percent of the residential housing stock has been destroyed. “What kind of city can it be?”
Ms. Kushnir, a model, described the persistent fear of being there for the last three weeks: “Every day is like a new birth. That is, you do not know whether you make it home or not.”
After she arrived to Urzuf, she had her first proper meal in weeks. But her mind was occupied with new pressing questions, she said:
“How will it be possible to get somehow to a safe place in Ukraine? Where is it safe in this country? How it will be possible to go abroad, where it can be safe for us?”