Some of the towns and cities struck include Severodonetsk, Rubizhne, Lysychansk, Kreminna and Ivanivka, Serhii Haidai, the head of the Luhansk regional military administration said in a statement.
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Two people died in Severodonetsk, residents of Lysychansk and Toshkivka were injured, four people were rescued, he said.
"There is no centralized water supply in Rubizhne, Popasna, Severodonetsk, part of the Hirske community and in Lysychansk. Twenty-eight settlements remain without gas supply and 22 without electricity."
Ukrainian forces had also fought off attempts by Russian troops to bypass their positions near the settlements of Popasna and Novotoshkivske, Haidai said in a separate statement.