Both Lviv and Krementchuk have been spared from the violence plaguing eastern Ukraine, where pro-Russian separatists are locked in a deadly battle against Ukrainian forces.
Sadovyi is a key figure in Ukraine’s pro-European protests that led to the downfall of former president Viktor Yanukovych in February.
“To my knowledge, no rocket launchers have been used to fire shots in Lviv,” said Sadovyi.
Lviv, a city with a population of 750,000 close to the Polish border, is a nationalist bastion of Ukrainian-speakers.
Oleg Babayev, mayor of the central-eastern city of Kremenchuk was killed not far from his home, the interior ministry said on Saturday.
In the other attack, the house of Andrii Sadovyi, mayor of the western city of Lviv, was hit by a rocket fired late on Friday.
No one was in the house at the time of the strike, his office said in a statement as local police launched a probe into what they described as a “terrorist attack”.