Dmytro Butriy, the acting head of the Kherson region military administration, said 44 settlements in the largely occupied area have been liberated.
Butriy gave no timescale. A Ukrainian offensive in Kherson began in May and has since recovered a number of villages, but no towns of any size.
Butriy said at a news briefing that the settlements were still suffering as they were under constant Russian bombardment.
"We urge people to evacuate to protect themselves and their families. Russian occupiers are not human," he said.
Butriy alleged the Russians had shot civilian cars in convoys as they tried to leave the region. CNN has previously reported on the shelling of convoys of civilian vehicles as they have tried to leave Russian-occupied areas.
Butriy also claimed "there were times when civilians were discovered dead with traces of torture."
Deputy Prime Minister Iryna Vereshchuk said "people can leave the occupied territories of Kherson region through the occupied Crimea or through [the] Vasylivka [checkpoint] towards Zaporizhzhia. It is necessary to leave, despite the fact that it is difficult. It is much more dangerous to stay in the occupied territory than to dare to go through all the checkpoints and leave."
Other Ukrainian officials have said it's increasingly difficult for people to leave through the Russian checkpoint at Vasylivka, with people spending several days waiting to get through.