A town in east Ukraine came under shellfire by pro-Russian rebels on Wednesday, amid fears that they are launching a counter-offensive on government-held parts of the region.

In response to outgoing fire early Wednesday, rebel forces lobbed at least 10 shells at the government-held town of Novoazovsk. Plumes of black smoke rose above the town, which was hit repeatedly shelled Tuesday, injuring four residents in a local hospital, according to the town's mayor, Oleg Sidorkin.

The renewed fighting came a day after the Russian and Ukrainian leaders met in Minsk, Belarus, to discuss the escalating crisis in east Ukraine.

Despite a one-on-one session between Vladimir Putin and Petro Poroshenko that lasted over two hours, there was no indication of a swift resolution to the fighting that has dragged on since April and claimed at least 2,000 civilian lives.

After the talks, Ukraine's president said Putin had accepted the principles of a peace plan for the region. The Russian leader, however, insisted that only Kiev could secure a cease-fire deal with the pro-Moscow separatists.

"This is not our business," Putin said of any cease-fire plan. "This is Ukraine's business."

Novoazovsk lies on the Azov Sea on the road that runs from Russia to the major Ukrainian port of Mariupol and west to Crimea, the Black Sea peninsula annexed by Russia earlier this year.

The latest shelling has raised fears that the separatists are aiming to take control of a strip of land that would link Russia to Crimea.