Russian forces allowed a first convoy of cars to escape Ukraine's besieged port of Mariupol on Monday after 10 days of failed attempts to relieve civilians dying under relentless bombardment.
The southeastern port, totally surrounded by Russian troops since the first week of the invasion, has suffered the worst humanitarian impact of the war, with hundreds of thousands of people sheltering in basements without food, water or shelter.
Local Ukrainian authorities say as many as 2,500 civilians have died so far in the city, a toll that cannot be independently confirmed. Russia denies targetting civilians.
"At one o'clock (1100 GMT) the Russians opened a checkpoint and those who have cars and fuel began to leave Mariupol in the direction of Zaporizhzhia," Andrei Rempel, a representative of the Mariupol city council who is now in Zaporizhzhia, a Ukrainian-held city further north, told Reuters.
"In the first two hours, 160 cars left. There are probably already many more now. The city continues to be bombed but this road is not being shelled. We don't know when the first cars can get to Zaporizhzhia as there are still many Russian checkpoints that need to be passed."
The city council said the convoy had already passed Berdyansk, a Russian-held city about 85 km from Mariupol.
"There is also confirmation that a ceasefire is currently holding along the humanitarian corridor that has been established," it said.
Obtaining safe passage for aid to reach Mariupol and civilians to get out has been Kyiv's main demand at several rounds of talks. All previous attempts at a local ceasefire in the area have failed.
'It's hard,' says negotiator
Russian and Ukrainian delegations held a fourth round of talks on Monday - by video link this time rather than in person in neighboring Belarus as in the past - but no new progress was announced.
"Communication is being held yet it's hard," tweeted Ukrainian negotiator Mykhailo Podolyak, who had earlier created some hope of headway by saying on Sunday that Russia was beginning to talk "constructively".
The talks had paused for the day but would resume on Tuesday. Russia "still has a delusion that 19 days of violence against (Ukrainian) peaceful cities is the right strategy", he said.
Nineteen days into Russia's invasion, its troops have still failed to capture any of Ukraine's 10 biggest cities, despite hammering several of them with relentless bombardment.
Drone video footage released by Ukrainian forces in Mariupol, the last Ukrainian-held city on the Azov Sea coast, showed a desolate wasteland of bombed-out buildings, many in flames, with smoke pouring into the sky.
Robert Mardini, Director General of the International Committee of the Red Cross (ICRC), which has a team on the ground in Mariupol, described "the level of fear, of despair" there.
"People are running out of water, electricity, gas for heating, access to medical services - the situation is really untenable, unbearable for civilians, and they really want a safe passage," he told Reuters.
Russian forces have been bearing down on the capital Kyiv from the northeast and northwest, but have made little progress so far towards the capital itself, despite heavy fighting that has reduced suburbs on the outskirts to rubble.
In Kyiv itself, an apartment block was hit by a missile overnight, killing at least one person, officials said.
"The staircase was not there anymore, everything was on fire," apartment resident Maksim Korovii said.
He and his mother did not know what to do, he said.
"So we ran out to the balcony. We managed to put on whatever clothes we had at hand and made our way from balcony to balcony and in the end, we climbed down by the next building's entrance."
Russia denies targeting civilians, saying it is conducting a "special operation" to demilitarise and "denazify" Ukraine. Ukraine and Western allies call this a baseless pretext for a war of aggression.
In Donetsk, held since 2014 by Russian-backed separatists, Russia's defense ministry said at least 20 people had been killed and 28 wounded by what it said was a Ukrainian missile with a cluster charge. It released footage of a missile on a busy street and vehicles destroyed by shrapnel.
Ukraine accused Russia or its allies of carrying out that attack themselves as a pretext: "It is unmistakably a Russian rocket or another munition," Ukrainian military spokesman Leonid Matyukhin said.
Reuters could not verify either account.
Pregnant woman dies in Mariupol
The Ukrainian foreign ministry said a pregnant woman who was photographed being evacuated wounded from a maternity hospital in Mariupol bombed by Russia last week had since died along with her unborn baby. Reuters was not able to verify this.
Despite video showing at least two pregnant women being carried out of the ruins, Russia has said the hospital was not used at the time and had been occupied by Ukrainian fighters.
The invasion has sent more than 2.8 million people fleeing across Ukraine's borders and trapped hundreds of thousands in besieged cities.
Global financial markets rallied on Monday on hopes for progress from the talks. Stocks rose while oil prices gave up some of their massive recent gains.
Russia is the world's biggest exporter of combined oil and gas, and Russia and Ukraine together supply nearly a third of the world's grain exports, as well as metals and chemicals used worldwide in industry and agriculture.
The war has caused a surge in commodity prices, threatening the global recovery at a time when inflation in the developed world is already at its highest since the 1980s and many poor countries are facing a food crisis.
Russia itself has been cast into economic isolation never before visited on such a big economy.
According to several U.S. officials, Russia has asked China for military equipment. Moscow and Beijing both denied this.
U.S. National Security Adviser Jake Sullivan, who met China's top diplomat Yang Jiechi in Rome on Monday, warned Beijing it would "absolutely" face consequences if it helped Moscow evade sanctions.