Russian troops are seeking to lay siege to the Ukrainian city of Mariupol and cut it off from electricity, food, water, heating and transportation, its mayor said Thursday.

"They are trying to create a blockade here, just like in Leningrad," Vadym Boichenko said in a statement referring to the horrific seige of Russia's second largest city by the Nazis during World War II, which left hundreds of thousands dead.

"These bastards couldn’t find a way to break us. So now they are trying to prevent us from repairing electricity, water and heating supply," Boichenko said, adding that Russian troops also damaged the rail link.

"They destroyed the trains so that we could not evacuate our women, children and elderly people," he added.

One week into the invasion, Russian troops have been advancing on Ukraine's southern front, having seized Kherson, a Black Sea city of 290,000 people, after a three-day siege that left it short of food and medicine.

Mariupol, an important port city of some 400,000 people east of Kherson on the Azov Sea, has been left without water or electricity in the depths of winter.