•Its general staff said that "in order to preserve the lives of Ukrainian defenders, a decision was made to withdraw".
•It said the Russians had multiple advantages in artillery, aircraft, manpower and other forces.
Ukraine's military has confirmed that the eastern city of Lysychansk has fallen to Russian forces.
"After heavy fighting for Lysychansk, the defence forces of Ukraine were forced to withdraw from their occupied positions and lines," the army general staff said.
Earlier Russia's Defence Minister Sergei Shoigu said his forces had captured Lysychansk and taken full control of Luhansk region.
Ukraine's troops were outgunned there.
Its general staff said that "in order to preserve the lives of Ukrainian defenders, a decision was made to withdraw".
It said the Russians had multiple advantages in artillery, aircraft, manpower and other forces.
Earlier, the head of Russia's Chechen Republic, Ramzan Kadyrov, published video apparently showing Chechen fighters in the centre of Lysychansk.
Further west, the Ukrainian-held city of Slovyansk came under heavy shelling, with at least six people killed.
It is in Donetsk region, which with Luhansk forms the industrial Donbas.
Just before he launched the war, President Vladimir Putin recognised all of Luhansk and Donetsk as independent of Ukraine. Russian proxy forces began an insurgency there in 2014.
Just over a week ago Russian troops captured Severodonetsk, a city reduced to ruins by weeks of Russian bombardment.