Russian forces on Wednesday targeted the southern Ukraine city of Zaporizhzhia, where thousands of refugees are taking shelter after escaping the besieged port city of Mariupol, regional officials said.

"Civilian objects have been bombed for the first time in Zaporizhzhia," the regional governor Alexander Starukh wrote on the Telegram social media platform.

"The rockets landed in the area of the Zaporozhye-2 railway station," he added, specifying that there were no casualties.

The city of Zaporizhzhia is the first safe port of call for those fleeing Mariupol.

Many then head to the country's west, to Poland or other bordering countries. 

Mariupol is facing a humanitarian catastrophe according to aid agencies, since heavy bombardment has left some 400,000 inhabitants with no running water or heating, and food running short.

Around 20,000 people managed to leave the encircled port city Tuesday through a humanitarian corridor agreed with Russian forces.

Taking Mariupol, which is situated 55 kilometres (34 miles) from Russia's border, would mark a strategic breakthrough for President Vladimir Putin.

The city lies between territory held by Russian-backed separatists in the Donbas region and the Crimean peninsula, which was annexed by Moscow in 2014 and from where it has launched its assault on key southern towns.