Russian forces began direct assaults on Severodonetsk on May 27 despite not yet having fully encircled the town, reported by the American Institute for the Study of the War (ISW).
They will probably try to occupy the territory in the city itself.
Russian forces have performed poorly in operations in built-up urban terrain throughout the war to date and are unlikely to be able to advance rapidly in Severodonetsk itself.
The occupiers in Lyman appear to be dividing their efforts—attacking both southwest to support stalled forces in Izyum and southeast to advance on Siversk.
"They will likely struggle to accomplish either objective in the coming days," the statement said.
In Popasna, the occupiers seek to advance north to support the encirclement of Severodonetsk, rather than advance west to Bakhmut.
Positions northeast of Kharkiv remain largely static, with no major attacks by russian or Ukrainian forces.
"Russian forces continue to fortify their defensive positions along the southern axis and advance efforts to integrate the Kherson region into russian economic and political structures," ISW added.
The Head of the Luhansk Regional Military Administration Serhey Haiday declared that rushists’ [translator's note - russian+fascist] fakes about the encircled Severodonetsk don't correspond to reality.
The Ministry of Defense said that the main goal of the russian federation is to encircle Ukrainian troops near Lysychansk and Severodonetsk and reach the administrative border of the Luhansk region.
The SES stressed that the enemy was using tactics of total destruction in the Luhansk region.