The strike had left a gaping hole in the police station in Ukraine's Lysychansk, one of a barrage of increasingly heavy Russian attacks on this eastern city where soldiers were busy Tuesday digging defensive positions.

The police station was hit on Monday night after Lysychansk endured heavy shelling that left at least one dead, adding to the "catastrophic destruction" in the strategic industrial city across the river from Severodonetsk in the eastern Donbas region.

Lugansk regional governor Sergiy Gaiday said the city was "very heavily shelled" throughout the day and was also hit by air strikes, badly damaging the police station and nearby apartment blocks.

The police station, which is on a side street leading down to the river, suffered a "direct hit" during the night that wounded 20 police officers, special forces colonel Oleksandr Kutsepalenko told AFP.

He said there were nine direct hits in the neighbourhood around the police station, two caused by "rockets", with the strikes leaving "54 craters" in the surrounding area.

The wounded police officers were taken to Lysychansk hospital, which has no electricity.

Heavy bombardment of the city began in the early afternoon and continued into the night, police said.

And the sound of Grads firing could still be heard on Tuesday morning.

Despite the strike, the police station was still running Tuesday, it being one of the few public services still working in this devastated city with locals turning up to register deaths, get help contacting relatives or even use the toilet.

Regional and city officials also hold meetings there.

"Partition walls fell down and the doors were blown out," said a policeman who gave his nickname as Petrovich, showing the damage to the building.

Outside were three burnt-out police cars which went up in flames after shrapnel caused a gas cylinder to explode, he said.

The station was also hit in March but with lower-calibre weaponry, he said.

Closer to the frontline, police have dragged the wreckage of destroyed cars and vans into the streets to create a network of obstacles aimed at slowing any advance by the Russians.

A block of flats opposite the station also had a huge hole in its facade and there was a Russian missile lying in the yard.

A woman from the second floor had suffered "shrapnel injuries", Petrovich said, and the road outside was strewn with pages of school textbooks and a stuffed toy.

Along the road into the city, numerous Ukrainian military vehicles including tanks, ambulances and armoured personnel vehicles were going back and forth.

On a baking hot day, a military ambulance had pulled off the road to attend to a burst tyre, its back doors flung open to let in some air.

Inside, the paramedic pressed down on the bandages of a bleeding soldier, with another young soldier on a stretcher next to him.

As the situation became more desperate for those left inside the city, locals could still be seen venturing out on bikes or on foot to buy food and get water.

Several older residents surveying the damage said they had hoped to buy bread at a nearby bakery but heard it had also been shelled.

Others were filling plastic bottles with water only meant for household use from a tub near the main fire station.

"They consider us to be separatists because we stayed," said a pensioner called Igor, speaking of local officials and even the region's governor.

"We are normal people," insisted a younger woman, pushing a pram full of plastic bottles.

Several also complained that they hadn't received their pensions.