Russian forces continued their assault on eastern and southern Ukraine Wednesday, as officials urged remaining residents in the port city of Mariupol to evacuate. 

Kharkiv and Kramatorsk came under further attack, and Russia also said it had struck areas around Zaporizhzhia and Dnipro.

Explosions were heard in the southern city of Mykolaiv and a hospital was reported to have been shelled in the town of Bashtanka.

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Russian Defense Ministry spokesman Maj. Gen. Igor Konashenkov said Moscow’s forces bombarded numerous Ukrainian military sites, though those claims could not be independently verified.

A senior U.S. defense official, speaking on condition of anonymity, told The Associated Press that the Russians had added two more combat units, known as battalion tactical groups, in Ukraine. That brought the total number of units in the country to 78, all of them in the south and the east, up from 65 last week, the official said.

A European official, likewise speaking on condition of anonymity to discuss military assessments, said Russia also has 10,000 to 20,000 foreign fighters in the Donbas region.

Military experts said the Russians’ goal is to encircle Ukrainian troops from the north, south and east.

The Kremlin declared weeks ago that its main target was the mostly Russian-speaking Donbas, where Moscow-backed separatists have been fighting Ukrainian forces for eight years.

Russian President Vladimir Putin said Wednesday that Russia will "act consistently" to make sure that life in Donbas "normalizes," calling the war necessary to protect "[his] people" there.

"All these eight years, bombing, artillery strikes and hostilities continued there. And of course, it was very, very hard for people," he said. "The goal of the operation is to help our people living in Donbas."

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More bombs were dropped on Mariupol – a key part of Russia's offensive – and Mayor Vadym Boychenko called on people to leave the city. 

"Do not be frightened and evacuate to Zaporizhzhia, where you can receive all the help you need – food, medicine, essentials – and the main thing is that you will be in safety," he wrote in a statement issued by the city council.

Boychenko said buses would be used for the evacuation and asked people who had already left Mariupol to contact relatives still in the city.

Deputy Prime Minister Iryna Vereshchuk said Wednesday that there is a "preliminary" agreement to operate a so-called humanitarian corridor route westward to Zaporizhzhia.

The corridor could be used by women, children and older people from Wednesday afternoon local time, she said on Telegram.

There was no immediate confirmation on the evacuation from the Russian side, which issued a new ultimatum to the Ukrainian defenders to surrender Wednesday. 

A previous ultimatum was ignored.

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The Kremlin’s spokesman said Russia has presented Ukraine with a draft document outlining its demands as part of peace talks and is now awaiting a response.

A Ukrainian presidential adviser said that Kyiv was reviewing the proposals.

The Associated Press contributed to this report.