Ukraine says its forces are enduring intense Russian shelling in the eastern city of Lysychansk, but denies claims that they are surrounded.
It is the last Ukrainian-held city in Luhansk, part of the industrial Donbas region. Russia captured the nearby city of Severodonetsk last month.
Russia has also fired more missiles at cities in the north and south.
The southern city of Mykolaiv – on a key route to the port city of Odesa – was shaken by several explosions.
The Russian defence ministry said its air force had destroyed five Ukrainian command posts and several ammunition dumps, but that claim has not been independently verified.
The blasts came a day after the Russians killed more than 20 people in a missile strike on a block of flats near Odesa.