Ukrainian President Volodymyr Zelenskyy has stressed his country will stage all-out resistance to Russian forces, which have launched a fierce offensive in eastern Ukraine.

Russia's defense ministry claimed on social media on Wednesday that its forces broke through Ukrainian defenses in a part of the Luhansk region, and pushed back Ukrainian troops by up to three kilometers.

Zelenskyy said in a video message on Tuesday that the situation on the frontline, especially in the Donetsk and Luhansk regions, remains extremely difficult.

He noted that Ukrainian troops are under attack in Bakhmut and other strongholds in Donetsk.

Zelenskyy said it is literally a battle for every meter of Ukrainian land.

"Every meter won there is a defense of our entire country," he said.

Britain's defense ministry posted on Twitter on Wednesday, "Production is almost certainly falling short of the Russian Ministry of Defence's demands to resource the Ukrainian campaign and restore its longer-term defence requirements."