KRAMATORSK, July 5 - The governor of the last remaining eastern province partly under Ukraine’s control urged his more than 350,000 residents to flee as Russia escalated its offensive and air alerts were issued across nearly the entire country.

Gov. Pavlo Kyrylenko said that getting people out of Donetsk province is necessary to save lives and enable the Ukrainian army better to defend towns from the Russian advance, The Associated Press reported.

“The destiny of the whole country will be decided by the Donetsk region,” Kyrylenko told reporters in Kramatrosk, the province’s administrative center and home to the Ukrainian military’s regional headquarters.

“Once there are less people, we will be able to concentrate more on our enemy and perform our main tasks,” Kyrylenko said.

The governor’s call for residents to leave appeared to represent one of the biggest suggested evacuations of the war, although it’s unclear whether people will be willing and safely able to flee. According to the U.N. refugee agency, more than 7.1 million Ukrainians are estimated to be displaced within Ukraine, and more than 4.8 million refugees left the country since Russia’s invasion started Feb. 24.

President Volodymr Zelensky said air alerts were issued Tuesday night in nearly all of the country, in many places after a long period of relative calm during which people searched for an explanation.

You should not look for logic in the actions of terrorists,” Zelenskyy said in his nightly video address. “The Russian army does not take any breaks. It has one task — to take people’s lives, to intimidate people — so that even a few days without an air alarm already feel like part of the terror.”

Much of the military activity appeared concentrated in Ukraine’s east. The Kramatorsk governor said that because they house critical infrastructure such as water filtration plants, Russia’s main targets are now his city and a city 16 kilometers (10 miles) to the north, Sloviansk. Kyrylenko described the shelling as “very chaotic” without “a specific target ... only to destroy civilian infrastructure and residential areas.”

Sloviansk also came under sustained bombardment Tuesday. Mayor Vadim Lyakh said on Facebook that “massive shelling” pummeled Sloviansk, which had a population of about 107,000 before Russian invaded Ukraine more than four months ago. The mayor, who urged residents hours earlier to evacuate, advised them to take cover in shelters.

At least one person was killed and seven were wounded Tuesday, Lyakh said. He said the city’s central market and several districts came under attack, adding that authorities were assessing the extent of the damage.

The barrage targeting Sloviansk indicated Russian forces were advancing farther into Ukraine’s Donbas region, a mostly Russian-speaking industrial area where the country’s most experienced soldiers are concentrated.

Sloviansk has previously taken rocket and artillery fire during Russia’s war in Ukraine, but the bombardment picked up in recent days after Moscow took the last major city in neighboring Luhansk province, Lyakh said.

It’s important to evacuate as many people as possible,” he warned Tuesday morning, adding that shelling damaged 40 houses on Monday.

The Ukrainian military withdrew its troops Sunday from the city of Lysychansk to keep them from being surrounded. (ap/ez)