Russia has pulled back its forces from a strategically placed Black Sea island where troops have faced relentless Ukrainian attacks, but kept up its push to encircle the last bulwark of Ukraine's resistance in the eastern province of Luhansk.

Russia's Defence Ministry said it withdrew its forces from Snake Island off Ukraine's Black Sea port of Odesa in what it described as a "goodwill gesture".

Ukraine's military said the Russians fled the island in two speedboats following a barrage of Ukrainian artillery and missile strikes.

Russian Defence Ministry spokesman Lt Gen Igor Konashenkov insisted that the withdrawal was intended to demonstrate that "the Russian Federation wasn't hampering the United Nations' efforts to establish a humanitarian corridor for taking agricultural products from the territory of Ukraine".

Ukraine and the West have accused Russia of blockading Ukrainian ports to prevent the exports of grain, contributing to the global food crisis.

Russia has denied the accusations and claimed that Ukraine needs to remove sea mines from the Black Sea to allow safe navigation.

Turkey has sought to broker a deal on unblocking grain exports from Ukraine, but the talks have dragged on without any sign of quick progress with Kyiv voicing concern that Russia could use the deal to launch an attack on Odesa.

Russia took control of the island that sits on a busy shipping lane in the opening days of the war in an apparent hope to use it to control the area and use it as a staging ground for an attack on Odesa.

The island came to epitomise the Ukrainian resistance to the Russian invasion, when Ukrainian troops there received a demand from a Russian warship to surrender or face bombardment. "Russian warship", the answer came back, "go f*** yourself".

The Ukrainian defenders of the island were captured by the Russians but later freed as part of a prisoner exchange.

Since the island was taken, the Ukrainian military has relentlessly bombarded a small Russian garrison and air defence assets stationed there.

In the east of Ukraine on Thursday, Moscow kept up its push to take control of the entire Donbas region.

It is focused on the city of Lysychansk, the last remaining Ukrainian stronghold in the Luhansk province.

Russian troops and their separatist allies control 95% of Luhansk and about half of Donetsk, the two provinces that make up the mostly Russian-speaking Donbas.

The Ukrainian General Staff said that the Russian troops were shelling Lysychansk and clashing with Ukrainian defenders around an oil refinery on the edge of the city.

Luhansk governor Serhiy Haidai said that Russian reconnaissance units tried to enter Lysychansk on Wednesday, but were repelled by the Ukrainian forces.

He said the Russians were trying to block a major road used to deliver supplies and fully encircle the city.

"The Russians have thrown practically all their forces to seize the city," Mr Haidai said.

Speaking on a visit to Turkmenistan early on Thursday, Russian President Vladimir Putin said his goals in Ukraine have not changed since the start of the war.

He outlined these as "the liberation of the Donbas, the protection of these people and the creation of conditions that would guarantee the security of Russia itself".

Mr Putin made no mention of his original stated goals to "demilitarise" and "de-Nazify" Ukraine.

He denied Russia had adjusted its strategy after failing to take Kyiv in the early stage of the conflict.

"As you can see, the troops are moving and reaching the marks that were set for them for a certain stage of this combat work. Everything is going according to plan," Mr Putin said at a news conference in Turkmenistan.

Meanwhile, funerals are set to be held for some of the 18 people confirmed killed by Monday's Russian missile strike on a busy shopping centre in Kremenchuk.

Crews continued to search through the rubble in search of another 20 people who remain missing.

After the attack on the shopping centre, Ukrainian President Volodymyr Zelensky accused Russia of becoming a "terrorist" state. 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 Nato leaders they either had to provide Ukraine with the help it needed to defeat Russia or "face a delayed war between Russia and yourself."

In southern Ukraine, the death toll from Wednesday's Russian missile strike on an apartment building in Mykolaiv rose to six, according to governor Vitaliy Kim. Another six people were wounded.

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