Mariupol citizens are "begging to be saved" as the situation inside its last stronghold has become dire, the city's mayor has said. 

The United Nations has sought to broker an evacuation of civilians from the southern port city as around 100,000 people are believed to be trapped with little access to food, water and medicine. 

Mayor Vadym Boichenko said: “There, it’s not a matter of days. It’s a matter of hours.”

An estimated 2000 Ukrainian defenders, alongside 1000 civilians, are holed up at the Azovstal steel plant.

The Soviet-era steel plant has a vast underground network of bunkers able to withstand airstrikes. But the situation has grown more dire after the Russians dropped “bunker busters” and other bombs.

“Locals who manage to leave Mariupol say it is hell, but when they leave this fortress, they say it is worse,” the mayor said.

So far, Russia’s troops and the separatist forces appear to have made only minor gains.

In part because of the strength of Ukrainian resistance, the US believes the Russians are “at least several days behind where they wanted to be” as they try to encircle Ukrainian troops in the east, said the senior US defence official, who spoke on condition of anonymity to discuss the American military’s assessment.

As Russian troops try to move north out of Mariupol so they can advance on Ukrainian forces from the south, their progress has been “slow and uneven and certainly not decisive,” the official said.

The British Ministry of Defence offered a similar assessment, saying it believes Russian forces in Ukraine are probably suffering from “weakened morale”, along with a lack of unit-level skills and “inconsistent air support”.

Russian forces have “been forced to merge and redeploy depleted and disparate units from the failed advances in northeast Ukraine”, the ministry said in a tweet on Saturday as part of a daily report on the war. It did not say on what basis it made the evaluation.

UN spokesman Farhan Haq said the organisation was negotiating with authorities in Moscow and Kyiv to create safe passage.

This time, “we hope there’s a slight touch of humanity in the enemy,” the mayor said. Ukraine has blamed the failure of numerous previous evacuation attempts on continued Russian shelling.

Russian Foreign Minister Sergei Lavrov, told Saudi-owned Al-Arabiya TV that the real problem is that “humanitarian corridors are being ignored by Ukrainian ultra-nationals”. Moscow has repeatedly claimed right-wing Ukrainians are thwarting evacuation efforts and using civilians as human shields.

In further comments published on Saturday by China’s official Xinhua News Agency, Mr Lavrov said Russia has evacuated more than one million people from Ukraine since the war began, including more than 300 Chinese civilians.

Ukraine has accused Moscow of forcefully sending Ukrainians out of the country.

Mr Lavrov also said Russian and Ukrainian negotiators talk “almost every day” but blamed “the bellicose rhetoric and inflammatory actions of Western supporters of the Kyiv regime” for disrupting the discussions.

Fighting could be heard from Kramatorsk to Sloviansk, two cities about 11 miles apart in the Donbas. Columns of smoke rose from the Sloviansk area and neighbouring cities. At least one person was reported wounded in the shelling.

In his nightly video address, Volodymyr Zelensky accused Russia of trying to destroy the Donbas and all who live there.

The constant attacks “show that Russia wants to empty this territory of all people,” he said.

“If the Russian invaders are able to realise their plans even partially, then they have enough artillery and aircraft to turn the entire Donbas into stones, as they did with Mariupol.”

Ukrainian troops in the Luhansk region of the Donbas repulsed an attack by Russian airborne troops and killed most of their unit, the governor said.

“Only seven of the invaders survived,” governor Serhiy Haidai said on Friday on Telegram. The claim could not immediately be confirmed.

He did not say where the attack took place but said Russian forces were preparing for an attack on Severodonetsk.

In a neighbourhood on the outskirts of Kharkiv that is regularly shelled by Russian forces, some residents remain in their apartments, even though the buildings have charred gaping holes. There is no running water or electricity so they gather outside to cook on an open flame.

In the nearby village of Ruska Lozava, hundreds of people were evacuated after Ukrainian forces retook the city from Russian occupiers, according to the regional governor. Those who fled to Kharkiv spoke of dire conditions under the Russians, with little water or food and no electricity.

“We were hiding in the basement. It was horror. The basement was shaking from the explosions. We were screaming, we were crying and we were praying to God,” said Ludmila Bocharnikova.

Former US Marine Willy Joseph Cancel, 22, was killed on Monday while working for a military contracting company that sent him to Ukraine, his mother, Rebecca Cabrera, told CNN.

At least two other foreigners fighting on the Ukrainian side, one from Britain and the other from Denmark, have also been killed.