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Russia pressed on with its offensive in eastern Ukraine on Thursday after NATO branded Moscow the biggest "direct threat" to Western security and agreed plans to modernise Kyiv's beleaguered armed forces.

Ukrainian authorities said they were trying to evacuate residents from the frontline eastern city of Lysychansk, the focus of Russia's attacks where about 15,000 people remained under relentless shelling.

"Fighting is going on all the time. The Russians are constantly on the offensive. There is no let-up," regional Governor Serhiy Gaidai told Ukrainian television.

Russian troops had attacked the Lysychansk oil refinery on Thursday morning, Gaidai later wrote on Telegram.

The ambassador of the self-proclaimed Luhansk People's Republic told Russia's RIA news agency the Lysychansk oil refinery was now fully controlled by Russian and pro-Russian forces, and all roads to Lysychansk were also under their control.