Ukrainian forces, meanwhile, have struck a Russian military base in occupied southern Ukraine.

Belgorod Governor Vyacheslav Gladkov reported several explosions in the city of nearly 400,000, some 40km north of the border with Ukraine.

At least 11 apartment buildings and 39 houses were damaged, including five that were destroyed, Gladkov said on the Telegram messaging app.

Senior Russian lawmaker Andrei Klishas accused Ukraine of shelling Belgorod and called for a stern response.

"The death of civilians and the destruction of civilian infrastructure in Belgorod are a direct act of aggression on the part of Ukraine and require the most severe - including a military - response," Klishas wrote on Telegram.

Moscow has accused Kyiv of numerous attacks on Belgorod and other regions bordering Ukraine since Russia's February 24 invasion. Ukraine has not claimed responsibility but has described the incidents as payback and "karma" for Russia's actions.

In the Russian-occupied southern Ukraine city of Melitopol, Ukrainian forces hit a military base with more than 30 strikes on Sunday, the city's exiled mayor said in a video address on Telegram.

The base had been "taken out of action", Ivan Fedorov said.

A Moscow-installed official said several private residential houses near the airfield were damaged.

"Shells fell on the territory of the airfield. There were no casualties," Evgeny Balitsky, head of the Russia-installed council in the southern Zaporizhzhia region, wrote on Telegram.

The General Staff of Ukraine's Armed Forces said its air force had flown some 15 sorties "in virtually all directions of hostilities".

"About 20 units of enemy equipment and two field ammunition depots were destroyed."

Russia is focussed on driving Ukrainian forces out of Luhansk and Donetsk provinces in the Donbas, where Moscow-backed separatists have been fighting Kyiv since Russia's first military intervention in Ukraine in 2014.

Ukrainian troops describe intense artillery barrages on residential areas, especially around Lysychansk, the last holdout city in Luhansk.

"The Russians are strengthening their positions in the Lysychansk area, the city is on fire," Luhansk Governor Serhiy Gaidai said on Telegram. "They attacked the city with inexplicably brutal tactics."

Rodion Miroshnik, ambassador to Russia of the pro-Moscow self-styled Luhansk People's Republic, told Russian television, "Lysychansk has been brought under control," but added: "Unfortunately, it is not yet liberated."

Ukraine National Guard spokesman Ruslan Muzychuk told Ukrainian television the city remained in Ukrainian hands.

Oleksiy Arestovych, an adviser to Ukrainian President Volodymyr Zelenskiy, said Russian forces had finally crossed the Siverskiy Donets river and were approaching the city from the north.

"This is indeed a threat. We shall see. I do not rule out any one of a number of outcomes here. Things will become much more clear within a day or two," he said.

"The more Western weapons come to the front, the more the picture changes in favour of Ukraine." Ukraine has repeatedly appealed for more weapons from the West, saying its forces are heavily outgunned.

Far from the eastern fighting, Russia said it had hit army command posts in Mykolaiv near the vital Black Sea port of Odesa, where the mayor on Saturday had reported a number of powerful explosions.

"The Russian occupiers are launching systematic rocket attacks in the direction of Mykolaiv," Ukraine's general staff said on Sunday.

Ukrainian authorities said another missile slammed into an apartment block near Odesa on Friday, killing at least 21 people. A shopping mall was hit on Monday in the central city of Kremenchuk, killing at least 19.

Australian Associated Press