KYIV (AFP, REUTERS) - Fighting between Ukrainian and Russian forces is “ongoing” in the strategic port of Mariupol, the local governor told CNN on Tuesday (April 19).

“There is fighting ongoing in Mariupol. This is street fighting,” Pavlo Kyrylenko governor of Ukraine’s eastern Donetsk region said.

Ukrainian forces there are “under heavy bombardment” but “continue to defend Mariupol”.

“There are certain districts where street fighting is continuing. I can’t say the Russians are controlling them,” Kyrylenko said, adding that the fighting was “not just small arms fighting, but also tank fighting”.

It is not possible to verify information given by either side given the scale of the fighting and lack of communications.

Russian forces are believed to have gradually pushed their way into the city, pinning Ukrainian troops down to giant factories near the port, which are equipped with vast underground tunnels.

Russia on Tuesday called on Ukrainian forces in Mariupol to “immediately” lay down their arms in a new ultimatum.

Its defence ministry said Ukrainian forces still holed up inside the devastated city’s main metallurgical plant Azvostal were facing a “catastrophic situation”. “Everyone who lays down their arms will be guaranteed survival,” it said.

Mariupol’s city council said on Monday that hundreds of civilians are also taking shelter in the factory.

“There are at least 1,000 civilians in the underground shelters of the metallurgical plant. Mostly women with children and the elderly,” it said on Telegram.

Russia last week claimed that more than a thousand Ukrainian soldiers had surrendered in Mariupol from a separate factory.

According to pro-Russian Ukrainian separatists, several hundred others are still fighting from within the huge Azovstal factory.

Thousands of civilians are believed to have been killed in the city, with those escaping speaking of harrowing conditions.

Earlier on Tuesday, Russian forces said they had opened a humanitarian corridor for Ukrainian troops who agreed to lay down their arms to leave Mariupol.

“The Russian armed forces opened a humanitarian corridor for the withdrawal of Ukrainian military personnel who voluntarily laid down their arms and militants of nationalist formations,” the defence ministry said, adding the safe corridor was opened at 2pm (7pm Singapore time).

To that end, Russian forces and troops of the self-proclaimed Donetsk People’s Republic “halted any military activity” around the Azovstal steelworks plant, Mikhail Mizintsev, head of the Russian National Defence Control Centre, said in a statement.

The ministry said the decision was made taking into account the “catastrophic situation” at the plant and “purely humanitarian principles”.

Humanitarian convoys have been deployed in “three directions” that include buses, cars and ambulances to transport and treat people.

Temporary accommodation and first aid facilities have also been set up, the ministry said.

Moscow urged Kyiv authorities to put pressure on the military “to stop the senseless resistance”.

“But realising that the commanders of Ukrainian units may not receive such orders and commands from the Kyiv authorities, we urge them to make such a decision on their own and to lay down their arms,” the ministry said.

Mariupol offers a land bridge between Moscow-controlled parts of eastern Ukraine and the Kremlin-annexed peninsula of Crimea.

The city has been encircled by Russian troops for weeks and has seen the fiercest fighting and most comprehensive destruction since Russia sent troops into Ukraine on Feb 24.

Ukraine said earlier on Tuesday there would be no humanitarian corridors to evacuate civilians in the country for a third consecutive day because there has been no agreement with Russia.

"Today, April 19, there will unfortunately be no humanitarian corridor," Ukraine's Deputy Prime Minister Iryna Vereshchuk wrote on Telegram.

"The intense bombardment of Donbas is continuing."

Vereshchuk had said that "the Russians refuse to open a corridor" to evacuate civilians from Mariupol towards Berdyansk.

"We're continuing the difficult negotiations for humanitarian corridors in the Kherson and Kharkiv regions", in the south and east respectively, she added.