Kyiv, Ukraine - Russia's President Vladimir Putin has abandoned his plan to have his invading forces storm a sprawling steel plant in Mariupol, where the Ukrainian city's last defenders are holding out.

Mariupol has been under relentless Russian siege for weeks. The Azovstal factory, which has a large network of underground areas, is the only remaining stronghold of Ukrainian resistance in Mariupol.

Putin was told by Defense Minister Sergei Shoigu on Thursday morning that, except for the plant, the south-eastern city was firmly under Russian control.

"The remaining Ukrainian combat units have entrenched themselves on the industrial site of the Azovstal factory," Shoigu said in the meeting that was broadcast on state television.

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According to Shoigu's account, the Ukrainian units are completely blockaded. The minister assured that the factory should be captured in the next three to four days.

Putin said he was rescinding his earlier order to have the steel plant stormed as it was not worth the potential loss of Russian lives. He said that troops should instead continue their blockade.

"There is no need to climb into those catacombs and crawl underground beneath those industrial facilities," Putin said.

"Block this industrial area so that even a fly can't get in or out."

No holdouts have left the factory via the humanitarian corridors offered by Russian, the minister said. Earlier, the Ukrainian side had proposed negotiations on the fate of the fighters and the rescue of civilians who had also sought refuge in the factory.

According to Russian information, around 2,500 Ukrainian and foreign fighters are still at the Azovstal works. Ukrainian reports say around 1,000 civilians are sheltering there, too.

Putin congratulated Shoigu on the successful operation to "liberate" Mariupol and told him to pass on his praise to the troops.

Mariupol was encircled by Russian troops shortly after the start of the war, ordered by Putin on February 24. The city has been almost completely levelled by the Russian bombardment.

The city on the Sea of Azov lies on the route between Crimea, which was annexed by Russia in 2014, and the areas in eastern Ukraine controlled by pro-Russian separatists.

Mariupol had about 400,000 inhabitants before the war. Thousands of civilians are feared dead after the long siege and continuous shelling.

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Russia has refocused its offensive on eastern Ukraine after withdrawing from areas around Kyiv.

All food stores have been destroyed by Russian attacks on the eastern city of Sievierodonetsk, the governor of the Luhansk region, Serhiy Haidai, said on social media.

"In Sievierodonetsk there is not a single intact storehouse left," Haidai said on Thursday. Residents now could only be fed using humanitarian aid supplies.

In addition, several houses in Rubizhne and Novodruzhesk were destroyed, Haidai said. Both cities are considered to be heavily contested.

In Kharkiv, at least two high-rise buildings in the north-eastern district of Saltivka and several parked cars caught fire after explosions, the Ukrainian news portal Ukrainskaya Pravda reported.

In the Dnipropetrovsk region, the neighbouring towns of Zelenodolsk and Velyka Kostromka came under heavy fire, the head of the local military administration wrote on Facebook.