The situation in the Ukrainian controlled eastern region of Donbas is "tense", a regional governor said Monday, asking people to evacuate as the army braced for a Russian advance.

Since Russia withdrew its troops near the capital Kyiv in the north and said it would focus on the "liberation" of the Donbas, residents have been living in fear of a major military offensive.

Families fleeing the eastern city of Kramatorsk in the Donbas region
Families fleeing the eastern city of Kramatorsk in the Donbas region AFP / FADEL SENNA

"We are firmly in control of all the territory... but the situation everywhere is tense," the governor of the eastern Donetsk region Pavlo Kyrylenko told journalists in the city of Kramatorsk.

"The most difficult situation is in the direction of Izyum where we expect the situation to escalate," Kyrylenko said, referring to a city recently captured by Russian forces in the neighbouring Kharkiv region.

Locals fear a major Russian military offensive
Locals fear a major Russian military offensive AFP / FADEL SENNA

"The enemy is bombing everywhere... a number of places along the line of control have been destroyed by bombardments," he said.

The Kyiv government has said it expects the situation to get worse as Russian troops seek to encircle Ukrainian forces, arranged since 2014 along the frontline between Donetsk to the south and Lugansk in the east -- the capitals of the two pro-Russian, breakaway "republics" of the same name -- and now from Izyum to the northwest.

Roughly four trains, carrying about 2,000 people, have been leaving Kramatorsk every day
Roughly four trains, carrying about 2,000 people, have been leaving Kramatorsk every day AFP / FADEL SENNA

The de facto capital of the Ukrainian-controlled part of Donetsk, Kramatorsk sits between the pincers of the Russian army.

Some 700,000 people remain in the Ukrainian-controlled zone
Some 700,000 people remain in the Ukrainian-controlled zone AFP / FADEL SENNA

"I've said it before and I will say it again: the civilian population needs to leave the area now," Kyrylenko said.

"We will share the logistical details of these evacuations. It's an gradual process, not something we can do in a day... but the situation is going to become more difficult, that's for sure," he added.

While refusing to share the specifics of the evacuation, Kyrylenko said 146,000 people had "already left the region" by Sunday.

A further 700,000 remained in the Ukrainian-controlled zone, he added.

"If the enemy respected the rules of war, the message would be different. As it is, we want as few citizens as possible to stay here, until the situation stabilises," the governor said.

In Kramatorsk, hundreds of people again gathered at the train station to travel to the west of the country.

Roughly four trains, carrying about 2,000 people, have been leaving the city every day for the past few days, with the operation managed by volunteers.

"Of course, we are aware of the concentration of enemy forces" in the east around Kramatorsk, Kyrylenko said.

Following the events in the town of Bucha, to the northwest of Kyiv, where dozens of civilians were found dead after Russian troops withdrew, "we can expect everything from the enemy", the governor said.