Scores of people who had been sheltering under a steel plant that is the last redoubt for Ukrainian forces in Mariupol have managed to at last leave, after enduring weeks under brutal siege in the destroyed port city.

The UN confirmed on Sunday that a “safe-passage operation” to evacuate civilians had begun, in coordination with the International Committee of the Red Cross, Ukraine and Russia, but declined to give further details in order to protect people.

As many as 100,000 people are believed to be in the blockaded city, which has endured some of the most terrible suffering of the Russian invasion. These include 1,000 civilians and 2,000 Ukrainian fighters thought to be sheltering in bunkers and tunnels underneath the Soviet-era Azovstal steelworks, the only part of the ruined city not taken by Russian forces.

After enduring a vicious weeks-long siege that forced people into confinement in basements, without food, water, heat or electricity, Russian forces closed in, leaving the steelworks as the last remaining stronghold. Vladimir Putin decided not to storm the plant, but called on Russian troops to blockade the area “so that a fly can’t get through”.

On Sunday, Ukraine’s president Volodymyr Zelenskiy said about 100 civilians were being evacuated from the ruined steelworks to the Ukrainian-controlled city of Zaporizhzhia. Zelenskiy’s chief of staff Andriy Yermak suggested the evacuations could go further than just the civilians holed up in the steelworks. “This is just the first step, and we will continue to take our civilians and troops out of Mariupol,” he wrote on Telegram.

Earlier, Reuters reported that more than 50 civilians in separate groups had arrived from the plant on Sunday in Bezimenne, a village about 20 miles (33km) east of Mariupol in territory controlled by Russian-backed separatists. The group arrived in buses with Ukrainian number plates as part of a convoy with Russian forces and vehicles with UN symbols.

News of the evacuation came as the US House speaker, Nancy Pelosi, met Zelenskiy in Kyiv, where she pledged enduring support for his country’s “fight for freedom”. Pelosi, whose visit was not announced beforehand, is the highest-level US official to meet the Ukrainian president since the war began.

Earlier this weekend, a senior soldier with the Azov regiment at the steelworks said 20 women and children had managed to get out. “We are getting civilians out of the rubble with ropes – it’s the elderly, women and children,” Sviatoslav Palamar told Reuters. On his Telegram channel, Palamar called for the evacuation of the wounded: “We don’t know why they are not taken away and their evacuation to the territory controlled by Ukraine is not being discussed.”

Russia’s defence ministry said on Sunday that 80 people, including women and children, had left the Azovstal works, according to the state news agency Ria Novosti.

The UN secretary general, António Guterres, said on Thursday when meeting Zelenskiy in Kyiv that intense discussions were under way to evacuate the Azovstal plant.

Russian forces have obliterated the once thriving port city of Mariupol, a major target for Moscow because of its strategic location near Crimea, which Russia annexed in 2014.

In his Sunday blessing, Pope Francis repeated his implicit criticism of Russia, as he said Mariupol had been “barbarously bombarded and destroyed”. Addressing the faithful at St Peter’s Square in Rome, the pope said he suffered and cried “thinking of the suffering of the Ukrainian population, in particular the weakest, the elderly, the children”.

Meanwhile, Zelenskiy released footage on Sunday of an earlier meeting between him, Pelosi and the US House representatives Jason Crow, Jim McGovern, Gregory Meeks and Adam Schiff. The US speaker pledged America’s support “until the fight is done”.

“We are visiting you to say thank you for your fight for freedom,” she said in video footage released on Zelenskiy’s Twitter account. “And that your fight is a fight for everyone, and so our commitment is to be there for you until the fight is done.”

Speaking at a press conference in Poland on Sunday, Pelosi said the US would hold its resolve, after being asked whether Washington was concerned about its support provoking a Russian reaction. “Let me speak for myself: do not be bullied by bullies,” she said. “If they are making threats, you cannot back down.”

Crow, a Democrat, armed forces veteran and member of the House intelligence and armed services committee, said he came to Ukraine with three areas of focus: “weapons, weapons and weapons.”

“The United States of America is in this to win and we will stand with Ukraine until victory is won,” he said.

Last week Joe Biden called for a $33bn (£26bn) package of military, humanitarian and economic support for Ukraine, more than doubling the level of US assistance to date. The US president asked Congress to immediately approve the aid, which dwarfs Ukraine’s entire defence budget.

While the US is increasing support for Ukraine, Germany’s chancellor rejected criticism that Berlin was not doing enough. In an interview with Bild am Sonntag, Olaf Scholz said he took decisions “fast and in concert with our partners”.

Meanwhile it emerged that the EU is looking at banning Russian oil imports from the end of 2022, in the latest effort to cut funds to Vladimir Putin’s war machine. Germany announced on Sunday it had made sharp reductions in its dependency on Russian fossil fuels, slashing oil imports from Russia to 12%, compared to 35% before the Russian invasion. Russian gas imports to Europe’s biggest economy have dropped to 35% from a pre-invasion figure of 55%.

Ukraine is now looking to China, as well as other permanent members of the UN security council, to provide security guarantees. In an interview with the Chinese state news agency Xinhua released on Sunday, Ukraine’s foreign minister, Dmytro Kuleba, said the proposal for China to provide a security guarantee was “a sign of our respect and trust in the People’s Republic of China”.

On the 67th day of the war, Russia continued its refigured campaign to seize parts of southern and eastern Ukraine, after failing to take Kyiv. Russia’s defence ministry said on Sunday it had attacked an airfield near Odesa and claimed to have destroyed a hangar that contained weapons provided by foreign countries. “High-precision Onyx rockets at a military aerodrome in the Odesa region destroyed a hangar with weapons and ammunition from the United States and European countries, and also destroyed the runway,” said a spokesperson for the Russian defence ministry, quoted by Ria Novosti. The report has not been independently verified.

Meanwhile, the governor of Kharkiv warned residents on Sunday not to leave shelters because of “intense shelling”. Oleh Synyehubov asked residents in the north and eastern districts of the city, especially Saltivka, not to leave their shelters unless it was urgent.

In his nightly video address on Saturday, Zelenskiy urged Russian troops not to fight in Ukraine, saying even their generals expected that thousands more of them would die.

He accused Moscow of recruiting new soldiers “with little motivation and little combat experience” so that units gutted early in the war can be thrown back into battle. “Every Russian soldier can still save his own life,” Zelenskiy said. “It’s better for you to survive in Russia than to perish on our land.”

As the first civilians were reported to have left the Azovstal plant, pictures showed a dire situation for the several thousand who remained.

Video and images shared with the Associated Press by two Ukrainian women who said their husbands were among the fighters refusing to surrender at the plant showed unidentified men with stained bandages, while others had open wounds or amputated limbs.

A skeleton medical staff was treating at least 600 wounded people, said the women, who identified their husbands as members of the Azov regiment of Ukraine’s national guard. Some of the wounds were rotting with gangrene, they said.

In the video the men said that they were eating just once daily and sharing as little as 1.5 litres of water a day among four people, and that supplies inside the besieged facility were depleted.

AP could not independently verify the date and location of the video, which the women said was taken in the last week in the maze of corridors and bunkers beneath the plant.

The women urged that Ukrainian fighters also be evacuated alongside civilians, warning they could be tortured and executed if captured. “The lives of soldiers matter, too,” Yuliia Fedusiuk told the news agency.

Associated Press contributed to this report.