Several explosions were heard on the outskirts of Lviv in western Ukraine at 15.30 on Saturday, Swedish time.
Five people are said to have been injured in the shelling, Reuters reports, citing local authorities.
No residential buildings should have been hit, according to the city mayor.
Pictures from the city showed heavy smoke development near the city's nearly 200 meters high TV towers, and aircraft alarms must have sounded in the city.
Several media outlets report that the TV tower has been hit.
A fuel depot must have hit and was still burning at 6 p.m.
TV pictures show how the extinguishing work is in full swing.
Lviv's governor Maksym Kozytskyy states that there have been two rocket attacks within the city limits.
He said in an earlier statement that three powerful explosions had been heard near the city center.
An official from the district administration also states that three explosions were heard.
"Everyone should stay calm and stay indoors," Regional Governor Maksym Kozytskyy said in a statement.
"A giant cloud of smoke"
Norwegian TV 2's reporter Kjetil Iden on site in Lviv reports on powerful explosions.
- From the roof of the hotel we see a giant cloud of smoke.
It is unclear what the goal was, he says.
Dagens Nyheter's correspondent Emma Bouvin had just returned to the hotel and went down to the shelter when the plane alarm went off.
The bangs were then suddenly heard over the city, she says.
Many refugees in the city
Lviv in western Ukraine has about 700,000 inhabitants and is located about 80 kilometers from the border with Poland.
It is a city where many refugees have come to seek refuge.
Explosions on the outskirts of the city have been reported earlier in the war, but Lviv has so far not suffered any major Russian attacks since the invasion of Ukraine began on 24 February.
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Hear TV2's reporter on site in Lviv.