Ukrainian officials have reported further shelling by Russian forces and civilian casualties in parts of the Donetsk and Luhansk regions, which have become the focus of Russian attacks.
Serhii Haidai, head of Luhansk regional military administration, said the cities of Severodonetsk, Lysychansk, Kreminna, Novodruzhesk and Rubizhne had been targeted again, with 12 residential buildings struck in the last day.
"Unfortunately, there were casualties in Lysychansk -- one man died, three more people were injured," Haida said. "The number of missile and air attacks on the Luhansk region has increased significantly.
Yesterday Lysychansk was bombed from planes and there was a missile attack."
"It is most difficult to evacuate people from the cities of Popasna and Rubizhne," he said, as they were partially occupied by Russian forces. "Our troops repel constant attacks. We can't go to certain areas of cities and pick up people due to constant shelling."
"In the cities of Kreminna, Severodonetsk and Lysychansk evacuation takes place daily," Haidai said, adding it can sometimes be as many as 2,000 people.
He said that hospitals are still operating in Lysychansk and Severodonetsk.
Haidai said that heavy rains could impede Russian efforts to advance.
"Within last two days they began to collect hundreds of units of heavy equipment, pulling it closer to the front line. This suggests that the offensive should begin today and tomorrow, but it is raining today. According to the forecast, it will rain for several days."
He said the rains would force vehicles to use roads, "and this makes an easy target for our defenders. I hope the rains slows down the offensive."
Ukrainian officials say Russian attacks by air are moving further west to the borders of the Donetsk and Luhansk regions.
Mykola Lukashuk, head of Dnipropetrovsk Regional Council, said that the night in the Dnipropetrovsk region was "restless."
"We had two air attacks on Synelnykiv district at the border of Zaporizhzhia and Donetsk regions," Lukashuk said, adding there were no casualties.
The General Staff of the Armed Forces of Ukraine said Tuesday that Russian forces continued to regroup along Ukraine's eastern borders and said it expected further ground attacks towards Popasna in Luhansk region and Kurakhove in Donetsk, "with the aim of reaching the administrative boundaries of Donetsk region."
It accused Russian forces of "placing their military equipment and troops directly in residential facilities," as well as in "agricultural enterprises, energy and social infrastructure facilities."
The Armed Forces claimed that six Russian attacks in the east had been foiled Monday and tanks, armored vehicles and artillery systems had been destroyed.
As the fighting in the east continues, the Ukrainian Deputy Prime Minister Iryna Vereshchuk announced nine evacuation corridors Tuesday, including from Mariupol and Berdiansk on the southeast coast, and Severodonetsk, Rubizhne and Lysychansk.