Meanwhile, a senior US official warned that Russia is planning to annex large portions of eastern Ukraine this month and recognise the southern city of Kherson as an independent republic.
Michael Carpenter, US ambassador to the Organisation for Security and Cooperation in Europe, said that those suspected actions are “straight out of the Kremlin’s playbook” and will not be recognised by the United States or its allies.
In Mariupol, more than 100 people — including elderly women and mothers with small children — left the rubble-strewn Azovstal steelworks on Sunday and set out in buses and ambulances for the Ukrainian-controlled city of Zaporizhzhia, about 230 kilometres to the northwest, according to authorities and video released by the two sides.
Mariupol Deputy Mayor Sergei Orlov told the BBC that the evacuees were making slow progress and would probably not arrive in Zaporizhzhia on Monday as hoped. Authorities gave no explanation for the delay.
At least some of the civilians were apparently taken to a village controlled by Russia-backed separatists. The Russian military said some chose to stay in separatist areas, while dozens left for Ukrainian-held territory.
In the past, Ukraine has accused Moscow’s troops of taking civilians against their will to Russia or Russian-controlled areas. The Kremlin has denied it.
The Russian bombardment of the sprawling plant by air, tank and ship picked up again after the partial evacuation, Ukraine’s Azov Battalion, which is helping to defend the mill, said on the Telegram messaging app.
Mr Orlov said high-level negotiations were underway among Ukraine, Russia and international organisations on evacuating more people.
The steel-plant evacuation, if successful, would represent rare progress in easing the human cost of the almost 10-week war, which has caused particular suffering in Mariupol. Previous attempts to open safe corridors out of the southern port city and other places have broken down, with Ukrainian officials accusing Russian forces of shooting and shelling along agreed-on evacuation routes.
Before the weekend evacuation, overseen by the United Nations and the Red Cross, about 1000 civilians were believed to be in the plant along with an estimated 2000 Ukrainian defenders. Russia has demanded that the fighters surrender; they have refused.
As many as 100,000 people overall may still be in Mariupol, which had a pre-war population of more than 400,000. Russian forces have pounded much of the city into rubble, trapping civilians with little food, water, heat or medicine.
Some Mariupol residents got out of the city on their own, often in damaged private cars.
As sunset approached, Mariupol resident Yaroslav Dmytryshyn rattled up to a reception centre in Zaporizhzhia in a car with a back seat full of youngsters and two signs taped to the back window: “Children” and “Little ones.”
“I can’t believe we survived,” he said, looking worn but in good spirits after two days on the road.
“There is no Mariupol whatsoever,” he said.
“Someone needs to rebuild it, and it will take millions of tons of gold.”
He said they lived just across the railroad tracks from the steel plant.
“Ruined,” he said. “The factory is gone completely.”
Anastasiia Dembytska, who took advantage of the cease-fire to leave with her daughter, nephew and dog, said she could see the steelworks from her window, when she dared to look out.
“We could see the rockets flying” and clouds of smoke over the plant, she said.
With most of Mariupol in ruins, a majority of the dozen Russian battalion tactical groups that had been around the city have moved north to other battlefronts in eastern Ukraine, according to a senior US defence official who spoke on condition of anonymity to describe the Pentagon’s assessment.
Ukrainian President Volodymyr Zelenskyy had said he hoped more people would be able to leave Mariupol in an organised evacuation on Monday. The city council told residents wanting to leave to gather at a shopping mall to wait for buses.
Mr Zelenskyy told Greek state television that remaining civilians in the steel plant were afraid to board buses because they feared they would be taken to Russia. He said he had been assured by the UN that they would be allowed to go to areas his government controls.
Also Monday, Mr Zelenskyy said that at least 220 Ukrainian children have been killed by the Russian army since the war began, and 1570 educational institutions have been destroyed or damaged.
In other developments, European Union energy ministers met Monday to discuss new sanctions against the Kremlin, which could include restrictions on Russian oil. Some Russia-dependent members of the 27-nation bloc, including Hungary and Slovakia, are wary of taking tough action.
Thwarted in his bid to seize Kyiv, the capital, Russian President Vladimir Putin has shifted his focus to the Donbas, Ukraine’s eastern industrial heartland, where Moscow-backed separatists have been battling Ukrainian forces since 2014.
Mr Carpenter, the US ambassador to the OSCE, cited information that Russia is planning “sham referenda” in the so-called Donetsk and Luhansk “people’s republics” that would attach the entities to Russia. He also said there were signs that Russia would engineer an independence vote in Kherson.
He noted that local mayors and legislators there have been abducted, that internet and cellphone service had been severed and that a Russian school curriculum is soon to be imposed. Ukraine’s government has said Russia also has introduced the ruble as currency there.
Russia said Monday it struck dozens of military targets in the region in the past day. It said it hit concentrations of troops and weapons and an ammunition depot near Chervone in the Zaporizhzhia region, west of the Donbas.
Ukrainian and Western officials say Moscow’s troops are raining fire indiscriminately, taking a heavy toll on civilians while making only slow progress.
The governor of the Odesa region along the Black Sea Coast, Maksym Marchenko, said on Telegram that a Russian missile strike Monday on an Odesa infrastructure target caused deaths and injuries. He gave no details. Mr Zelenskyy said the attack destroyed a dormitory and killed a 14-year-old boy.
Ukraine said Russia also struck a strategic road and rail bridge west of Odesa. The bridge was heavily damaged in previous Russian strikes, and its destruction would cut a supply route for weapons and other cargo from neighbouring Romania.
The attack on Odesa came eight years to the day after deadly clashes between Ukrainian government supporters and protesters calling for autonomy in the country’s east. The government supporters in 2014 firebombed a trade union building containing pro-autonomy demonstrators, killing over 40 people.
Also on Monday, Ukraine claimed to have destroyed two small Russian patrol boats in the Black Sea.
Mariupol, which lies in the Donbas, is key to Russia’s campaign in the east. Its capture would deprive Ukraine of a vital port, allow Russia to establish a land corridor to the Crimean Peninsula, which it seized from Ukraine in 2014, and free up troops for fighting elsewhere.
Britain’s Defence Ministry said it believes more than a quarter of all the fighting units Russia has deployed in Ukraine are now “combat ineffective” — unable to fight because of loss of troops or equipment.