Russia's defense ministry says it has agreed to evacuate wounded Ukrainian soldiers from a steel plant in the eastern Ukrainian city of Mariupol.

The announcement came on Monday amid continued fierce fighting between Russian and Ukrainian forces in the eastern parts of the country.

The ministry said Russian troops backed by missiles destroyed Ukrainian munitions depots and command posts in Donetsk, Luhansk and Kharkiv.

The governor of Kharkiv told local media that Ukrainian troops have reached the border with Russia and are regaining lost territory.

A high-ranking US Defense Department official unveiled an analysis backing up the governor's claims. The official also suggested that Russian forces are failing to make significant progress in the eastern regions, amid heavy shelling between the two sides.

On Monday, the Russian defense ministry announced that it had reached an agreement with the Ukrainians on the removal of wounded soldiers from the Azovstal steelworks.

The Ukrainians have been demanding their evacuation.

The ministry said those soldiers will be taken to a medical facility in Donetsk. The facility is under the control of pro-Russian forces.

Meanwhile, Mariupol Mayor Vadym Boichenko claimed that Russians are trying to block the evacuation of civilians from the city.

The mayor said in an online interview with NHK on Monday that about 90 percent of the city is occupied by Russian forces, and that more than 100,000 civilians remain stranded. He said Russia's military is trying to bring evacuees back to the city, offering them places to live.

He also suggested that some civilians may remain trapped in the steel plant. He said attacks on the steelworks continued from the air and sea, and that a huge fire broke out there following a Russian attack, which he said may have involved the use of modern weapons.