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Russian drones targeted the capital Kyiv and other cities in the early hours of Tuesday, hitting critical infrastructure in Lviv in the west, officials said.
The attacks on the capital and Zaporizhzhia in the south were both described as massive.
Ukraine's air force said 35 drones were launched and all but three shot down.
No-one was hurt in the attack on Lviv, the local authority said, after explosions rang out early on Tuesday.
But the head of the regional authority, Maksym Kozytskyi, said a critically important target had been hit three times by Iranian Shaheed drones and fire had broken out.
More than 20 drones were fired at the capital in waves from Russian territory to the north and from the coast of the internal Sea of Azov in the south-east, according to the air force. Kyiv authorities said it was the first such incident in 18 days.
Zaporizhzhia was attacked by a number of Iskander-M ballistic missiles, officials said, adding that nobody had been hurt. Three drones were also shot down over the southern region of Mykolaiv, the governor said.
The Zaporizhzhia region is the focus of much of the Ukrainian military's current offensive to recapture territory seized by Russia at the start of its full-scale invasion in February 2022.
Deputy Defence Minister Hanna Malyar said hours earlier that Ukrainian forces had recaptured the village of Piatykhatky as they try to break through Russia's front line in the southern region. She said it was the eighth Ukrainian village to be recaptured in the past week. There has been no independent confirmation of the latest developments.
In his nightly TV address, Ukrainian President Volodymyr Zelensky said that in some areas the military was moving forward while in others they were holding positions against Russian attack.
The defence minister said Ukraine's push had advanced some 7km (4.3 miles) in two directions in Zaporizhzhia, towards the occupied southern cities of Melitopol and Berdyansk.
The exiled mayor of Melitopol, Ivan Fedorov, said residents had seen Russian forces leave the Kherson region further west for the front line in Zaporizhzhia.
Melitopol and Berdyansk lie on a coastal route from Russia to Crimea seen as critical to the Russian military because the bridge over the Kerch Strait from Russia to occupied Crimea is largely avoided by supply lorries. A Russian MP said earlier this month that the bridge was not considered secure but the "land corridor" was operating normally.
Western intelligence officials say Russian troops have moved away from the front line in Kherson since areas around the Dnipro river were flooded after the Kakhovka dam was destroyed on 6 June.