Russian attacks have destroyed an oil refinery in Ukraine's central Poltava region and struck "critical infrastructure", most likely a fuel depot, near the port city of Odesa, local officials said on Sunday.

Odesa, on the Black Sea coast, is a key Black Sea port and the main base for Ukraine's navy. It has been a focus for Russian forces because if it is taken it would allow Moscow to build a land corridor to Transdniestria, a Russian-speaking breakaway province of Moldova that hosts Russian troops.

Dmytro Lunin, governor of the Poltava region, said on television that the Kremenchug oil refinery had been destroyed in a rocket attack on Saturday. Kremenchug is 350 kilometres (220 miles) northeast of Odesa.

"The fire at the refinery has been extinguished but the facility has been completely destroyed and can no longer function," Lunin said.

Reuters could not independently confirm the refinery had been hit.

Earlier, Russia's defence ministry said missile strikes by its military destroyed an oil refinery and three fuel storage facilities near Odesa on Sunday, adding that the facilities were used by Ukraine to supply its troops near the city of Mykolaiv.

Vladyslav Nazarov, an officer of Ukraine's South Operational Command, said on Telegram: "Russia began with a missile strike. The Odesa region was among the priority targets. The enemy continued its vile practice of strikes against critical infrastructure."

"Smoke is visible in some areas of the city. All relevant systems and structures are working ... No casualties reported."

Odesa Mayor Gennadiy Trukhanov said on television the situation was now "under control", adding: "Homes, civilian infrastructure, roofs have suffered damage".

He added that Russia would likely use an opportunity to attack Transdniestria sooner or later but that Ukrainian forces were aware of the threat.

Vika, a local resident who declined to give her surname, said it was not "a good morning for Odesa".

"We woke up to powerful explosions near our home. There was smoke, the children were in a panic, the windows were blown in ... it was terrifying," she told Reuters.

"'Russian peace', we are completely not happy that it has come and we ask you to leave."

Russia denies targeting civilians.

Russian forces invaded Ukraine on Feb. 24 in what the Kremlin calls a "special military operation" to demilitarise and "denazify" its neighbour. Ukraine rejects that as a baseless pretext for a war of aggression.