Russia has targeted Ukraine's southern Black Sea regions of Odesa and Mykolaiv with airstrikes, hitting private buildings and port infrastructure with missiles fired from long-range bomber aircraft, the Ukrainian military said.

In the Odesa region, buildings in coastal villages were hit and caught fire, Ukraine's Operational Command South said on Facebook. A Ukrainian air force spokesman said long-range Russian Tu-22M3 bombers and Su-30 and Su-35 fighter jets launched the strikes from the Black Sea. In the Mykolaiv region, port infrastructure was targeted despite agreements intended to allow grain shipments to resume from Ukraine's Black Sea ports.

Hours after the strikes, a Moscow-installed official in southern Ukraine said the Odesa and Mykolaiv regions would soon be "liberated" by Russian forces, just like the already occupied Kherson region further east.

Firefighters work at a damaged residential building following Russian shelling on the outskirts of Odesa, Ukraine. Photo / AP

"The Kherson region and the city of Kherson have been liberated forever," Russian state news agency RIA Novosti quoted the region's Russia-appointed official, Kirill Stremousov, as saying.

On the diplomatic front, Russia's foreign minister repeated his insistence that Moscow was ready to hold talks with Ukraine on ending the war, though he again claimed that Kyiv's Western allies oppose a deal.

"We never refused to have talks, because everybody knows that any hostilities end at the negotiating table," Russian Foreign Minister Sergey Lavrov said during a trip to Uganda.

He said negotiations have gone no further since a meeting between the two sides in Istanbul at the end of March.

While Ukrainian officials have spoken of a possible counteroffensive in the south, the British Defence Ministry reported no indication a Ukrainian warship and a stockpile of anti-ship missiles were at Odesa's port, as Moscow claimed when it struck the site over the weekend.

The British ministry said Russia sees Ukraine's use of anti-ship missiles as "a key threat" limiting its Black Sea Fleet.

"This has significantly undermined the overall invasion plan, as Russia cannot realistically attempt an amphibious assault to seize Odesa," the ministry said. "Russia will continue to prioritise efforts to degrade and destroy Ukraine's anti-ship capability."

It added, "Russia's targeting processes are highly likely routinely undermined by dated intelligence, poor planning, and a top-down approach to operations."

In other military developments, Russian shelling over the previous 24 hours killed at least three civilians and wounded eight in Ukraine, the Ukrainian president's office said.

A woman walks among apartment buildings destroyed by Russian shelling on the outskirts of Odesa, Ukraine. Photo / AP

In the eastern Donetsk region, where the fighting has focused in recent months, shelling continued along the entire front, with Russian forces targeting some of the region's largest cities, Bakhmut, Avdiivka and Toretsk, the presidential office said.

Donetsk regional governor Pavlo Kyrylenko accused Russian troops of using cluster munitions and repeated his call for civilians to evacuate.

"There is not a single safe place left. Everything is being shelled," Kyrylenko said in televised remarks. "But there are still evacuation routes for the civilian population."

The Institute for the Study of War, a Washington-based think tank, reported that Moscow was using mercenaries from the shadowy Wagner Group to capture the Vuhledar Thermal Power Plant on the northern outskirts of the Bakhmut region village of Novoluhanske.

But Russian forces have made "limited gains" there, Ukraine's General Staff acknowledged.

The main regional Russian focus for the moment is on capturing Bakhmut, which the Russian military needs to press its eastern offensive on Ukrainian strongholds in Donetsk, the cities of Sloviansk and Kramatorsk.

"Russian forces made marginal gains south of Bakhmut but are unlikely to be able to effectively leverage these advances to take full control of Bakhmut itself," the Institute for the Study of War said.

Russian forces continued to strike civilian infrastructure in Kharkiv, Ukraine's second-largest city, and the surrounding region in the country's northeast.

Kharkiv Governor Oleh Syniehubov said the strikes on the city resumed around dawn Tuesday and damaged a car dealership.

"The Russians deliberately target civilian infrastructure objects — hospitals, schools, movie theatres," Syniehubov told Ukrainian television. "Everything is being fired at, even queues for humanitarian aid, so we're urging people to avoid mass gatherings."

The Moldovan foreign ministry said Tuesday a Moldovan citizen was killed and another wounded in what it claimed was a Ukrainian attack on Russia's border with Ukraine. The unconfirmed report said the attack occurred at a border checkpoint in Russia's Bryansk region.

Responding to a comment by Lavrov that Moscow's overarching goal in Ukraine is to free its people from its "unacceptable regime", German Foreign Minister Annalena Baerbock said the Kremlin wants "the complete subjugation of Ukraine and its people".

"We must be prepared for this war — which Russia is conducting with absolute brutality, and is conducting in a way that no one else would — to last months," Baerbock said during a visit to Prague.

- Susie Blann, AP