Mayor Andriy Sadovyi said several missiles hit a facility for repairing military planes near the city’s international airport and also damaged a bus repair site.
No casualties were immediately reported in the strikes on the city, which has had its population swelled by some 200,000 people seeking refuge from attacks across Ukraine.
Lviv has largely been affected by the fighting - the majority of which has taken place in the east of Ukraine - but Lviv has become a hub for thousands of refugees fleeing the conflict, many arriving with serious injuries.
It is the closest the war has come to the historic city in western Ukraine.
Here is everything you need to know about it.
Where is Lviv?
Lviv is the largest city in Western Ukraine and the sixth-largest city in Ukraine overall, with a population of 717,510.
It is located about 40 miles east of the Polish border on the edge of the Roztochia Upland, a range of low and rolling hills in east-central Poland and western Ukraine.
During the city’s history, it has been ruled by many countries, androm 1434, it was the regional capital of the Ruthenian Voivodeship, part of the Kingdom of Poland.
Lviv would remain part of Poland until 1918 when, for a short time, it was the capital of the West Ukrainian People's Republic.
Between the two World Wars, the city was once again under Polish rule (this time as part of the Second Polish Republic), but after the German-Soviet invasion of Poland in 1939, Lviv became part of the Soviet Union.
In 1991, it became part of the independent nation of Ukraine, and remains one of the main cultural centres of Ukraine, with a historic city centre on the UNESCO World Heritage List.
Why has Russia attacked Lviv?
Armed forces minister James Heappey said on Friday the early-morning attack on the city that has swelled with people sheltering from elsewhere in Ukraine showed Russia was broadening its strikes.
Heappey said that “it’s very much a part of war that you would go after each others’ supply lines but clearly the airstrike on an airbase in western Ukraine last week and strikes on Lviv airport last night show that the Russians are starting to go after Ukrainian depth as well”.
BBC correspondent in Lviv, Jonah Fisher, said the area used to be considered a “safe haven”.
He said the shelling is possibly an attempt by Russian forces to “cut off the supply of weapons into the country”, as major routes tend to run via Poland.
It comes as British intelligence suggested Vladimir Putin’s invasion had made only “minimal progress” this week.
The Ministry of Defence said that Ukrainian forces were continuing to “frustrate” Moscow’s attempt to encircle cities despite heavy shelling.
Western officials have described the advance on Kyiv as remaining “bogged down” amid questions over whether Moscow would still mount an assault on the city, which had been its main objective.
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