* Fight for Mariupol has been biggest battle of war

* Putin says Russia has 'liberated' the city

* Mayor seeks "full evacuation" of Mariupol

KYIV, April 22

The mayor of Mariupol appealed on Friday for the "full evacuation" of the devastated southern Ukrainian city which President Vladimir Putin says is now controlled by Russian forces.

"We need only one thing - the full evacuation of the population. About 100,000 people remain in Mariupol," Mayor Vadym Boichenko said on national television.

Boichenko, who is no longer in Mariupol, did not provide any update on any fighting in or around the port city on the Sea of Azov.

The mayor told Reuters on Thursday that Putin alone can decide the fate of the civilians still trapped in Mariupol, scene of the worst humanitarian crisis of the war in Ukraine that began on Feb. 24.

Putin said on Thursday that Russian troops had "liberated" Mariupol, which would make it the biggest city to fall into Russian hands since the start of what Moscow calls a "special military operation".

But a contingent of Ukrainian fighters are still holding out in the underground bunkers of the Azovstal steel complex, alongside hundreds of civilians in desperate conditions, according to Ukrainian authorities.

Despite Boichenko's appeal, Deputy Prime Minister Iryna Vereshchuk said Ukraine was not attempting to establish any humanitarian corridors for civilians on Friday "due to the danger on the routes".

"To all those waiting to be evacuated: be patient, please hold on!" she wrote on Facebook.

Hopes of evacuating more civilians from the eastern town of Rubizhne, where there has been heavy fighting, were dashed by Russian artillery fire, regional governor Serhiy Gaidai said.

Russia did not immediately comment on the remarks by Vereshchuk or Gaidai. Moscow has denied targeting civilians and blames Ukraine for the repeated collapse of efforts to arrange humanitarian corridors for civilians.

ONE CONVOY MADE IT OUT

Citizens who did not flee during nearly two months of siege and fighting have suffered without electricity, heating or running water. Boichenko has said tens of thousands of residents have been killed. The figure cannot be verified.

Some civilians have escaped to other parts of Ukraine in private cars or on foot, and tens of thousands have been taken to Russia in what Moscow calls humanitarian evacuation and Kyiv says is illegal forced deportation.

A small convoy was able to leave Mariupol on Wednesday, and buses carrying 79 of the evacuees arrived on Thursday in the town of Zaphorizhzhia, about 230 km (160 miles) northwest of the port city.

The convoy was the first official bus convoy that was able to make it to Ukraine-controlled territory from the city since the start of the siege, Boichenko said, though it was smaller than originally planned.

Waving, smiling and some of them crying, the evacuees were met at the Zaphorizhzhia bus terminal by Red Cross officials and police. Clutching their possession in bags, they were ushered into a tent for registration.

One woman, a firefighter named Olena Zamyslova, had brought her dog with her.

"We were in the basement and they (Russians) started shelling us. Ukrainian soldiers visited us. They began to calm us down. They even went for a search of my cat during the night while there was shelling," she told Reuters.

"They helped me a lot. I've left the place with little of what I had."

Another evacuee, Valentyna Andryushenko, a social worker from Mariupol, said after she stepped off the bus: "They were bombing us from day one. They are demolishing everything. They just erase it (the city).