In a video address, the Ukrainian president said: “They have transitioned into a new stage of terror, in which they try to physically liquidate representatives of Ukraine’s lawful local authorities,”
The address from the president came after Kirill Timoshenko, the deputy head of Ukraine’s presidential office, posted a video on Telegram which claimed to show a group of armed men carrying mayor Ivan Fedorov across a square.
A Moscow-backed rebel group, the Luhansk People’s Republic, have claimed that there was a criminal case against Mr Fedorov.
The prosecutor’s office of the Luhansk People’s Republic accused him of “terrorist activities” and had claimed they had been looking for the mayor since Russia took the city, which has a population of 150,000 last month.
According to Mariupol officials 1,582 people had been killed in the 12 days since the siege began.
Mariupol’s mayor’s office called for Russian forces to lift the siege saying “There is a humanitarian catastrophe in the city and the dead aren’t even being buried.”
"And I hope that, and I have confidence in the armed forces of Ukraine, that that will not be happening anytime soon."
A member of Ukraine's parliament has said history is repeating itself as she referred to the world "averting their eyes" from Adolf Hitler before stepping in as the death toll increased.
Lesia Vasylenko told Times Radio: "I don't think I know that someday in the future it could be me or any of my 426 colleagues or any one member of our families.
"We knew this from day one that we are targets on a special Russian list, and there's the fate of each one of us is predetermined already in that list.
"When it will happen, if it will happen, I don't know.
"The history is just repeating itself time and time again, and I don't understand what is wrong with us humans and humanity why we don't learn from the lessons.
"It's so much easier to prevent death from happening, and destruction from happening, than to later restore it and deal with all the trauma."