Russian forces battled to surround the Ukrainian military's last stronghold in a long-contested eastern province as shock reverberated from a Russian airstrike on a shopping centre that killed at least 18 people in the central city of Kremenchuk on Tuesday.

Moscow's battle to wrest the entire Donbas region from Ukraine saw Russian forces pushing towards two Luhansk province villages south of the city of Lysychansk, while Ukrainian troops fought to prevent their encirclement.

The UK's Ministry of Defence said Russian forces were making "incremental advances" in their offensive to capture the city.

Lysychansk is the last major area of the province under Ukrainian control following the retreat of Ukraine's fighters from the neighbouring city of Sievierodonetsk.

Russian troops and their separatist allies control 95% of Luhansk and hold about half of Donetsk region, the other province that makes up the mostly Russian-speaking Donbas.

The latest assessment by the Institute For The Study of War, a think tank based in the US, said the Ukrainians were likely to be in a fighting withdrawal to seek more defensible positions while draining the Russian military forces of manpower and resources.

Meanwhile, crews continued to search through the rubble of the shopping centre in Kremenchuk where Ukrainian authorities said 20 people remained missing. Authorities in the city declared three days of mourning.

The blast from Tuesday's airstrike was so powerful, relatives may not be able to recover any trace of their loved ones' remains.

Ukrainian state emergency services press officer Svitlana Rybalko said that along with the 18 people killed, investigators had found fragments of eight more bodies. A number of survivors were being treated for injuries such as skull fractures and severed limbs.

"The police cannot say for sure how many (victims) there are. So we are finding not the bodies but the fragments of bodies," Ms Rybalko said.

"Now we are clearing at the very epicentre of the blast. Here, we practically cannot find bodies as such."

Several families stood by what was left of the Amstor shopping centre on Wednesday morning in hopes of finding missing loved ones. One young woman sat cross-legged on the ground weeping behind dark sunglasses.

"This is pure genocide," local resident Tatiana Chernyshova said while going to lay flowers at the site.

"Such things cannot happen in the 21st century. Peaceful people suffer."

"We need to engage everyone to help stop the war, help us fight these scum - these Russian aggressors," Ms Chernyshova said.

"It needs to be stopped by any means possible."

Following the attack, Ukrainian president Volodymyr Zelensky accused Russia of becoming "a terrorist" state carrying out "daily terrorist acts".

On Wednesday, he reproached Nato for not embracing or equipping his embattled country more fully.

"The open-door policy of Nato shouldn't resemble old turnstiles on Kyiv's subway, which stay open but close when you approach them until you pay," Mr Zelensky told Nato leaders meeting in Madrid, speaking by video link.

"Hasn't Ukraine paid enough? Hasn't our contribution to defending Europe and the entire civilisation been sufficient?"

He asked for more modern artillery systems and other weapons and warned the leaders they either had to provide Ukraine with the help it needed to defeat Russia or "face a delayed war between Russia and yourself".

Russian foreign ministry spokeswoman Maria Zakharova dismissed what she claimed was the Ukrainian government's "blatant provocation" in trying to blame the shopping centre missile strike on Russia's military.

"All these fakes, unfortunately, were replicated and distributed," Ms Zakharova said.

In southern Ukraine, a Russian missile strike in the city of Mykolaiv killed at least four people and injured five after a missile hit a multi-story apartment building on Wednesday, regional governor Vitaliy Kim said.

Mykolaiv is a major port in Ukraine's south and seizing it - as well as Odesa further west - would be key to Russia's object of cutting Ukraine off from its Black Sea coast.

Russia's defence ministry said in a statement that the missile strike on Mykolaiv targeted a base for training "foreign mercenaries", as well as ammunition depots.