Ukrainian President Volodymyr Zelenskyy has vowed to win back all the cities that Russian forces have taken, after the key eastern city of Severodonetsk was occupied.

Russian forces had been advancing on Severodonetsk and the city across a river, Lysychansk, in a bid to take full control of the eastern-most region of Luhansk.

The mayor of Severodonetsk admitted on Saturday that the city is now fully occupied by Russian forces.

Ukraine's military intelligence chief told the Reuters news agency that Ukrainian forces made a "tactical withdrawal" to fight from higher ground in Lysychansk.

The official was quoted as saying, "given the conditions, holding the defense in the ruins and open fields is no longer possible. "

The focus has now shifted to Lysychansk, where Russia said street battles began on Saturday after its forces had moved in from the south.

President Zelenskyy said on Saturday that in a half day, 45 Russian missiles hit wide areas, including the northern, southern and western parts of his country.

The president called for stepping up sanctions against Russia, and speeding up military aid from the West.

His top military commander wrote on social media that US-supplied advanced HIMARS rocket systems were now deployed and hitting targets in Russian-occupied parts of the country.