"Nine dead, nine wounded," the head of the regional administration, Vitaliy Koval, said on messaging app Telegram, adding that work was under way to free survivors trapped under the rubble in the village of Antopil.

Koval said at a briefing that two rockets hit the building early on Monday morning, Interfax-Ukraine news agency reported.

He posted pictures of firefighters using cranes to lift sections of shattered concrete and brick walls and carrying a stretcher.

Rivne is located around 200 kilometres northeast of Lviv, a city near Poland's border, which has become the exit point for many Ukrainians fleeing the country.