Lutsk, which had a pre-war population of over 200,000, is less than 100 kilometres (60 miles) from Ukraine's border with Poland.

Lutsk mayor Igor Polishchuk said on Telegram that "there are three dead and three wounded", adding that emergency services were on site.

Regional governor Yuriy Poguliaiko said earlier Tuesday that air defence forces had repelled overnight air attacks.

"But, unfortunately, we had a 'strike' at one of the industrial enterprises in the regional centre," he said on Telegram.

In March last year, four Ukrainian soldiers were killed and six wounded in Russian strikes on the Lutsk military airport.

About 150 kilometres (90 miles) south of Lutsk, in Lviv, mayor Andriy Sadovyi said "many missiles were shot down", but that "residential buildings got hit" in the strike.

"Fortunately, there were no casualties. Unfortunately, there is a lot of damage," he said on Telegram.

"More than 100 apartments were damaged, more than 500 windows were broken, and a kindergarten was destroyed" after a missile flew into its yard, he said.

He said four people were wounded but "there is no threat to their lives".

A supermarket ceiling collapsed "due to falling missile fragments", regional governor Maksym Kozytskyi said, adding that more than 10 homes were damaged.

Lviv has mostly been spared the daily bombardments that have hit other parts of Ukraine.

But in July, 10 people were killed in what Sadovyi said was the biggest Russian missile attack on the city's civilian infrastructure since the invasion.

UNESCO said that attack was the first to take place in an area protected by the World Heritage Convention and had damaged a historic building.

- Ukrainian gains -

On the frontline, the Ukrainian military said Monday it had pushed Russian forces out of pockets of territory in the east and south of the country, building on a gruelling counter-offensive launched two months ago.

Kyiv has acknowledged that movement against heavily fortified Russian positions has been slow and said it had gained only a clutch of land around the war-battered city of Bakhmut last week.

The gains came as Russia claimed its forces had progressed in the eastern Kharkiv region, undermining Kyiv's highly anticipated campaign.

Ukraine kicked off its counter-offensive against Russian forces in June after building up assault battalions and stockpiling Western-donated weapons.