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Watch: Ukraine reports first civilians killed in Lviv
Plumes of thick, black smoke were rising over Lviv after the explosions which were witnessed by reporters on the ground.
Lviv Mayor Andriy Sadovyi said seven people were killed and 12 wounded in overnight missile strikes
Lviv’s regional governor Maksym Kozytskyy said three hit military infrastructure facilities and one struck a tire shop.
Emergency teams were on site putting out the fiires caused by the strikes.
Lviv Mayor Andriy Sadovyi put the toll at six dead and 11 wounded, including one child.
Lviv has been spared much of the worst-hit violence after Vladimir Putin declared war on the country almost two months ago.
The city is about 70km from the border with Poland.
Russia has been increasing its strikes on weapons factories, railways and other infrastructure targets across Ukraine to wear down the country’s ability to resist a major ground offensive in the Donbas, military analysts have said.
Russian troops are determined to capture the Donbas where Moscow-backed separatists already control some territory.
Their latest efforts comes after its attempt to take the capital Kyiv failed.
Watch: Smoke billows out from Lviv after reports of blasts
Zelensky said in his nightly address to the nation: “We are doing everything to ensure the defence.”
The leader called for more air raid shelters and more anti-radiation medicines.
Asked if he was concerned about the prospect of a nuclear attack by CNN, Mr Zelensky said: “Not only me - all of the world, all of the countries have to be worried.”
He added: “Chemical weapons... They could do it, for them the life of the people [is] nothing. That’s why. We should think not be afraid, not be afraid but be ready.
“But that is not a question for Ukraine, not only for Ukraine but for all the world, I think.”