Athens on Wednesday launched an operation to evacuate Greek diplomats, journalists and other citizens from the Ukrainian city of Mariupol as Russian forces push further into the country.

A convoy of 21 cars with over 80 people had set out, accompanied by the ambassador to Ukraine, Greek public television ERT reported. 

A Greek foreign ministry source said the convoy would head west under Russian assurances of safety, picking up people from other cities including Dnipro and Zaporizhzhia.

"Mariupol today is under fire from the north and south, it is a surrounded city," junior foreign minister Miltiadis Varvitsiotis told ERT, warning the journey of 1,100 kilometres (685 miles) will be "difficult, even in terms of obtaining fuel".

"We believe that the Ukrainian authorities will show understanding," he added.

A group of 26 Greeks and family members were relocated from Odessa to Moldova on Monday, and another 50 Greeks and Cypriots from Kiev and Odessa were flown out of Romania with their families on Tuesday, the foreign ministry said.

The Greek migration ministry has said some 1,500 people have fled to Greece from Ukraine.

President Katerina Sakellaropoulou said the hotel industry was making preparations to help accommodate refugees from Ukraine.

Migration Minister Notis Mitarachi has also said a former migrant camp near the northern town of Serres had been set aside to accommodate people.

A migration ministry source said the Sindiki camp can accommodate up to 700 people.

But many members of Ukraine's ethnic Greek community of over 100,000 people do not want to abandon their homes.

"(Russian empress) Catherine the Great took us out of our Crimea homeland. We already lost one homeland, we don't want to lose another," Mariupol resident Athina Hatzinova told ERT on Wednesday.

"I'm staying with my mother. She's 83, and we don't have a mode of transport.

"From the first day, my mother said she's not leaving, I'm not leaving either," she said.

Greece says Russian airstrikes have killed nearly a dozen members of the ethnic Greek community.

Russia denies this and says Ukrainian forces are to blame.