Effectively declaring victory in the strategic port city after nearly two months of siege, Russian President Vladimir Putin said there was no point in trying to root out the defenders barricaded inside the sprawling factory.

"I consider the proposed storming of the industrial zone unnecessary," he told his Defence Minister Sergei Shoigu in a televised meeting at the Kremlin. "I order you to cancel it."

"There's no need to climb into these catacombs and crawl underground through these industrial facilities," he said.

"Block off this industrial area so that not even a fly can get through."

Shoigu estimated 2000 Ukrainian fighters remain inside the plant. Putin called on them to surrender, saying Russia would treat them with respect.

Overnight, Mikhailo Podolyak, Ukraine's chief negotiator, proposed talks be held inside Mariupol itself on the fate of its last defenders.

"Without any conditions. We're ready to hold a 'special round of negotiations' right in Mariupol," he tweeted late on Wednesday.

"One on one. Two on two. To save our guys, Azov (battalion), military, civilians, children, the living & the wounded. Everyone. Because they are ours. Because they are in my heart. Forever."

The city of 400,000 people on the Sea of Azov, under bombardment and siege since the war's earliest days, has been the scene of the heaviest fighting and worst humanitarian catastrophe of the conflict.

Ukraine says tens of thousands of civilians have died in the city that - other than the steel plant - Russia claims is effectively now under its control.

A commander of the Azov regiment rejected Russia's surrender demands.

In a video appeal, Svyatoslav Palamar called for "third parties" to guarantee the safety of hundreds of civilians sheltering in the factory's bunkers.

"Let me say that we do not accept the conditions set down by the Russian Federation on giving up our weapons and our defenders giving themselves up as prisoners," Palamar said.

Russia has blocked all efforts by Ukraine to send aid to Mariupol or buses to evacuate civilians to Ukrainian-controlled territory, and Kyiv accuses it of forcibly deporting tens of thousands of residents to Russia.

Moscow says Russia has taken in 140,000 civilians in humanitarian evacuations.

On Wednesday, Russian-backed forces organised a small convoy of buses to let some residents leave an area they control for Zaporizhzhia, in Ukrainian government-controlled territory.

The number of Ukrainian refugees who have fled to neighbouring countries surged past five million on Wednesday, and many millions more are displaced inside the country.

Mariupol is the link Moscow needs to provide a secure connection between territory held by the separatists it backs in eastern Ukraine's Donbas region and Crimea, the peninsula it seized in 2014.

It is also the main port of the Donbas, two provinces Moscow demands Ukraine fully cede to the separatists in what the Kremlin now describes as the war's main objective.

After failing to capture Kyiv last month and being forced to withdraw from northern Ukraine, Russia regrouped to launch a major new offensive this week in the Donbas, pushing from several directions to encircle Ukrainian troops.

Ukraine said Russian forces had failed so far to completely capture Rubizhne, a Donbas town that has been a focus of their advance.

On Tuesday, Ukraine said Russia had captured neighbouring Kreminna, while the cities of Kramatorsk and Kharkiv were also coming under sustained bombardment.

British military intelligence said Russian forces were keen to demonstrate significant success by May 9, the anniversary of the allied victory in Europe in World War II.

Putin said the first test launch on Wednesday of Russia's Sarmat intercontinental ballistic missile, a new addition to its nuclear arsenal, would "provide food for thought for those who, in the heat of frenzied aggressive rhetoric, try to threaten our country".

Australian Associated Press