Dmytro, a businessman who declined to disclose his last name, said: “You hear the words but it’s impossible to really take them in, to believe this is happening. It is hell on earth.”
A woman from Mariupol, Victoria, described how “three children I know died from dehydration”.
“It is the 21st century, and children are dying from dehydration in my city, they are starving now,” she told the BBC.
“My city is absolutely destroyed. Me, my family, all our friends, we don't have our homes now.
“All the buildings are destroyed and the shelling is continuing. It is on fire all the time, except a few hours at night.
“People stay in the basements but it doesn't save them. They're bombing so hard so they're destroying even the basements.
“They don't have water, we gathered snow several days ago of water.”
Former ITN Journalist Bill Neely tweeted that he was hearing “Horrifying reports” from the city.
He said “thirsty people” were “draining water from radiators” and there are “people eating dogs”.
Neely also said streams contaminated by rotting bodies while dogs fed on corpses in what is an “apocalyptic nightmare in a place where” a month ago “life was normal”.
A Russian air strike on March 10 destroyed the maternity hospital in the city, killing a woman and her unborn baby.
A harrowing picture showed the mother being stretchered from the hospital and she later screamed "kill me, kill me" when she found her baby was lost - then died herself.
Harrowing pictures show corpses being put in body bags and dumped in mass graves following heavy shelling.
Two "super powerful bombs" rocked Mariupol on Tuesday as Ukrainian authorities made a fresh attempt at rescuing civilians.
"It is clear that the occupiers are not interested in the city of Mariupol, they want to raze it to the ground, to reduce it to ashes," the authorities said.
Ukrainian leader Volodymyr Zelensky turned to Pope Francis for help, urging the pontiff to mediate in the conflict and to help end "human suffering".
It comes as Russian troops are allegedly raping women and slaughtering families hiding in their basements as they rampage through Ukrainian cities.
Anastasia Taran, 30, has accused Putin's brutal soldiers of raping women in the Russian -occupied city of Irpin - which has been under attack from Russia's invading forces for nearly a month.
Ukraine's foreign minister previously confirmed there had been reports of Putin's soldiers sexually assaulting Ukrainian women.
An elderly man carrying his remaining possessions through the street Credit: Maximilian Clarke / Story Picture Agency The twisted wrecks of cars in Mariupol Credit: AP Russian forces have been pounding the city Credit: Reuters