Ukrainian officials have acknowledged the loss of several communities near the city of Lysychansk, the only conurbation in Luhansk region they still control.
"The Russians are approaching Lysychansk, entrenching in nearby towns. The city is being shelled by aircraft," according to Serhiy Hayday, head of the Luhansk regional military administration.
Hayday acknowledged it was "difficult" in the area south of Lysychansk. "The enemy entered Toshkivka, which allowed it to increase fire on other settlements."
He said Russian forces were entrenched in several villages immediately to the south of Lysychansk, including Ustynivka, Pidlisne and Myrna Dolyna, and were advancing at Bila Hora. "It is not easy for our soldiers to keep the defense," he admitted.
Hayday's comments suggest that Ukrainian defenses around Lysychansk have begun to succumb to much greater Russian firepower, after weeks of bombardment.
He said that "street fights continue in Severodonetsk," where Ukrainian defenders still occupy a part of the Azot chemical plant.
But he said the Russians were trying to surround Ukrainian units in some areas (such as Borivske) near Lysychansk and Severodonetsk. Military analysts have said that the risk of a Russian advance from the south means that some Ukrainian troops could be cut off.
Hayday added: "Lysychansk is under heavy fire now. The city is shelled from artillery, tanks and aircraft. There are at least three wounded civilians there, several policemen were injured." He said the police and security service buildings were hit by missiles.
Throughout its campaign, Russia has used the tactic of intense bombardment before trying to take territory.
Elsewhere, the Ukrainian military's General Staff said Russia held up to three battalion tactical groups and airborne units in border areas as potential reinforcements.
Settlements near Kharkiv had been intensively shelled, it said. On Tuesday, 15 people were reported killed by artillery strikes in the area.
In the Donetsk region, the General Staff said that Russian forces were using multiple launch rocket systems "in order to create conditions for the resumption of the offensive on the city of Sloviansk."
But it also said that Ukrainian units had prevented the Russians advancing towards Bakhmut from the south.
Elsewhere, along active front lines that extend for more than 1,000 kilometers, the Ukrainians reported shelling of settlements in Donetsk and Zaporizhzhia regions.
The head of the Donetsk regional military administration, Pavlo Kyrylenko, said six children had been wounded and one person killed in shelling of Chasiv Yar. He said cluster munitions had landed on a beach at a lake in the town.