Ukraine and Russia carried out airstrikes along opposing Black Sea coastlines early Thursday, just hours after direct talks between the two sides ended without progress toward ending their nearly three-and-a-half-year war.

Russian forces staged the latest in a series of mass drone attacks on Ukraine's Black Sea port of Odesa, injuring at least four people and causing several fires as well as damage in the historic centre, a UNESCO world heritage site.

The famous Pryvoz market in Odesa was among the places hit, Regional Gov. Oleh Kiper said. "It is not just a place of trade, it is the living heart of Odesa," he added.

On Thursday morning, some residents were cleaning up shattered glass in the streets nearby.

"So what if the (drones) are flying? We will shoot them down; they will not break us," Yevhen, a 20-year-old student among those helping with the cleanup, told Reuters.