Fierce fighting has continued inside Mariupol’s Azovstal steelworks, the commander of Ukrainian forces in the plant said, as more civilians fled the city on evacuation buses following weeks of brutal bombardment that have reduced much of it to rubble.

Ukrainian forces were fighting “difficult bloody battles” against Russian troops for a second day, Denys Prokopenko, commander of the Azov regiment, said in a brief video released on Telegram late on Wednesday.

“I am proud of my soldiers who are making superhuman efforts to contain the pressure of the enemy … the situation is extremely difficult,” commander Denis Prokopenko said.

Earlier on Wednesday, David Arakhamia, the head of Ukraine’s ruling party in parliament, told RFE/RL that Russian forces had entered the plant, but he said that the country’s government remained in contact with the Ukrainian troops staging a last stand.

The Kremlin’s official spokesperson, Dmitry Peskov, denied reports that Moscow’s forces were trying to storm the plant. “The order was publicly given by [Vladimir Putin] to cancel the storming,” Peskov said. “There is no storming.”

Russia said its forces would cease firing at the factory on Thursday morning, and open a three-day humanitarian corridor for any civilians.

“The Russian armed forces will from 8am to 6pm (Moscow time, 0500 GMT to 1500 GMT) on May 5, 6 and 7 open a humanitarian corridor from the territory of the Azovstal metallurgical plant to evacuate civilians,” the defence ministry said.

“During this period, the Russian armed forces and formations of the Donetsk People’s Republic will unilaterally cease any hostilities.”

The Ukrainian president, Volodymyr Zelenskiy, said in a national address on Wednesday night that another 344 people had been rescued from the centre of Mariupol and its suburbs on Wednesday.

Zelenskiy said negotiations continued to rescue people trapped in the Azovstal steel works. “There are still civilians. Women, children,” he added.

It is not known whether any of the civilians trapped in the works, where about 200 people – including 30 -children – remain, were among those who got out on Wednesday..

On Tuesday, the Ukrainian MP Kira Rudik said 156 people had managed to leave Mariupol and reach the relative safety of Zaporizhzhia, 140 miles (230km) away, after at least 20 failed attempts to evacuate civilians from the Azovstal site.

She told Sky News the main goal of aid workers “is to make sure we get out all the children”, adding: “It’s about 30 children who are still there. The most complicated step would be with the wounded soldiers, because Russia is not allowing them to get out.”

Russia’s defence minister, Sergei Shoigu, said the remaining Ukrainian forces in the plant were “securely blocked along the entire perimeter”. He claimed repeated proposals to “release civilians and lay down their arms” had been ignored.

Ukraine on Wednesday accused Moscow of planning to stage a military parade in Mariupol on 9 May, when Russia traditionally celebrates its victory over the Nazis in the second world war with processions in dozens of cities.

“Mariupol will become a centre of ‘celebration’,” Ukraine’s military intelligence said in a statement on social media. “The central streets of the city are urgently being cleaned of debris, bodies and unexploded ordnance.”

It said an official from Russia’s presidential administration had already arrived in the city, now almost entirely under Russian control, for a “large-scale propaganda campaign. Russians will be shown stories of locals’ ‘joy’ at meeting the occupiers.”

Azovstal evacuees who arrived in Zaporizhzhia were emotional. “We are so thankful for everyone who helped. There was a moment we lost hope, we thought everyone forgot about us,” said Anna Zaitseva, holding her six-month-old baby.

Elyna Tsybulchenko, 54, said Russian forces “bombed like every second”. “Everything shook. Dogs barked and children screamed,” she told Agence France-Presse. “The hardest moment was when we were told our bunker would not survive a direct hit.”

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After failing to capture Kyiv, Moscow has refocused its efforts on gaining full control of Luhansk and Donetsk, which make up the eastern Donbas region, and securing a southern land corridor via Mariupol to occupied Crimea.

Ukraine’s defence ministry said Russia was raising the tempo of its offensive and that it had conducted nearly 50 airstrikes on Tuesday. A ministry spokesperson, Oleksandr Motuzyanyk, said artillery bombardments and airstrikes were also continuing on the Azovstal plant.

On Wednesday both sides reported Russian strikes on key transport infrastructure around the western city of Lviv, near Poland, and in Transcarpathia, bordering Hungary.

There were also fears the conflict could spill over into neighbouring Moldova. The European Council president, Charles Michel, offered the republic the EU’s “full solidarity” and support. “We plan to significantly increase our support to Moldova by providing its armed forces with additional military equipment,” he said during a visit.