On Wednesday, the Ukrainian military said it had so far staved off any major Russian advance into the north of Donetsk, but pressure is intensifying with heavy shelling on the city of Sloviansk and nearby populated areas.
It said Russian forces were bombarding several Ukrainian towns with heavy weaponry to enable ground forces to advance southward into the region and close in on Sloviansk.
"The enemy is trying to improve its tactical position...(They) advanced ... before being repulsed by our soldiers and retreating with losses," the Ukrainian military said in its evening note.
Other Russian forces, it said, aimed to seize two towns en route to the city of Kramatorsk, south of Sloviansk, and were also trying to take control of the main highway linking Luhansk and Donetsk provinces.
"We are holding back the enemy on the (Luhansk/Donetsk) border," Luhansk Governor Serhiy Gaidai told Ukrainian TV. Later, he said Luhansk was still not entirely occupied by Russian forces and that Russia had sustained "colossal losses."
"They will continue to try to advance on Sloviansk and Bakhmut. There is no doubt about that," he said.
Sloviansk Mayor Vadym Lyakh told a video briefing the city had been shelled for the last two weeks.
"The situation is tense," he said, adding that 17 residents had been killed there since Feb. 24.
Russia's defence ministry says it does not target civilians and on Wednesday said it was using high-precision weapons to take out military threats.
Ukraine has repeatedly pleaded with the West to send more weapons to repel the invasion that has killed thousands, displaced millions, and flattened cities.
"At last, Western artillery has started to work powerfully, the weapons we are getting from our partners. And their accuracy is exactly what is needed," Ukrainian President Volodymyr Zelenskiy said In his nightly video message.
'NO SAFE AREAS'
In the Donetsk city of Kramatorsk, which Russian forces are expected to try to capture in coming weeks, Ukrainian soldiers and a handful of civilians ran errands in green-painted cars and vans on Wednesday. Much of the population has left.
"It's almost deserted. It's spooky," said Oleksandr, a 64-year-old retired metal worker. He was unlikely to follow official advice to evacuate, he said, despite an increase in missile strikes.
"I'm not looking for death but if I encounter it it's better to be at home," he said.
Outside the Donbas, Ukraine's second largest city Kharkiv was being subjected to "constant" longer-range Russian shelling, Mayor Ihor Terekhov said on Ukrainian TV.
"Russia is trying to demoralise Kharkiv but it won't get anywhere," he said. Ukrainian defenders pushed Russian armoured forces well back from Kharkiv early in the war, and Terekhov said around 1 million residents remained there.
South of Kharkiv, the governor of Dnipropetrovsk said the region had been battered by missiles and shelling, while on the southern coast the port of Mykolaiv was also being heavily shelled, Oleksandr Senkevych, its mayor, told a briefing.
"There are no safe areas in Mykolaiv," he said. "I am telling the people... that they need to leave."
Reuters was unable to immediately verify battlefield reports.
Reuters