Russian forces are focusing their efforts on encircling the city of Lysychansk, the Ukrainian military's General Staff said early Thursday.
Russian forces already control the southern and eastern approaches to Lysychansk, and fighting continues close to the main highway southwest of the city, where a large oil refinery is situated.
The Russians are also trying to close in on the town of Bakhmut, some 50 kilometers (31 miles) west of Lysychansk, and have made some gains south of the town, the General Staff said Thursday.
If successful, they would potentially trap Ukrainian forces still defending lines in a pocket of territory in Luhansk and Donetsk regions.
"The enemy is partially successful, it is entrenching in the northern part of Klynove and near the E-40 highway," said the General Staff. "In order to maintain the pace of the offensive in this direction, the occupiers strengthened the group with one battalion tactical group."
Some Ukrainian officials have called the E-40 "the highway of life" because of its importance in resupplying troops and evacuating civilians, which would be greatly complicated if the Russians interdict the highway.
Elsewhere in Donetsk – near Sloviansk – the General Staff said that the Russians were still focused on assault operations north of the city and had moved more weapons and military equipment into the area.
Local Ukrainian officials have previously said that the Russians are reinforcing north of Sloviansk, one of several major cities in Donetsk that remain in Ukrainian hands.
The General Staff said that the Russians continued to shell Ukraine's northeastern Sumy region from across the border and had also brought a multiple launch rocket system into action.
Dmytro Zhyvytskyy, head of the Sumy region military administration, said three people had been killed.
The Russians had also carried out airstrikes, he said, using helicopters that shot missiles from the other side of the border. The town of Krasnopillya was "covered" with fire, he said.
In southern Ukraine, the Ukrainian military says that the Russians have added one battalion tactical group to forces south of Kryvyi Rih.
Yevhen Sytnychenko, head of Kryvyi Rih district military administration, said that the city's thermal power plant had been shelled but continued to operate.
"The goal of the Russians is to intimidate the civilian population," he said, adding that one man had been injured in the shelling of a village south of the city.
In the city of Dnipro, the bodies of two people had been recovered from the rubble of a transport depot hit on Tuesday, according to local authorities.