Ukraine said it saw possible room for compromise Tuesday in talks with Russia, while Moscow's forces stepped up their bombardment of Kyiv, and an estimated 20,000 civilians fled the desperately encircled port city of Mariupol by way of a humanitarian corridor. 

The fast-moving developments on the diplomatic front and on the ground came on the 20th day of Russia's invasion, as the number of Ukrainians fleeing the country amid Europe's heaviest fighting since World War II eclipsed 3 million. 

A top Ukrainian negotiator, presidential adviser Mykhailo Podolyak, described the latest round of talks with the Russians, held via videoconference, as "very difficult and sticky" and said there were "fundamental contradictions" between the two sides, but added that "there is certainly room for compromise." He said the talks will continue Wednesday. 

Earlier in the day, another aide to Ukrainian President Volodymir Zelenskyy, Ihor Zhovkva, struck a more optimistic note, saying that the negotiations had become "more constructive" and that Russia had softened its stand by no longer airing its demands that Ukraine surrender. 

In other developments, the leaders of three European Union countries — Poland, the Czech Republic and Slovenia — visited the embattled capital, arriving by train in a bold show of support amid the danger. 

Nuclear war 'only a few steps away' 

A senior officer in Britain's air force has uttered words none of us want to hear, warning that nuclear war is "only a few steps" away. 

British Air Marshal Edward Stringer was explaining the caution of Western leaders, including his own Prime Minister Boris Johnson and US President Joe Biden, who have imposed heavy sanctions on Russia and provided aid to Ukraine without intervening directly in the conflict. 

"It's no longer unthinkable," Stringer said, referring to nuclear war. 

"And it will certainly be weighing on the minds of those who are making all the political calculations at the moment. Hence the very straight and consistent line from Biden and all the other senior heads of state recently. 

"It is in the realms of possibility, and that is what people have to get their heads around." 

He said it was possible to "sketch a plausible chain of events" leading to nuclear war. 

"That's only a few steps, to get from where we are now to a confrontation that could see the use of nuclear weapons, which I think is a pretty terrifying prospect for anybody sensible." 

Women head home to aid war effort 

People wait in a line to board a train leaving for Lviv in Ukraine at the train station in Przemysl, Poland. Photo / AP 

While over three million people have fled Ukraine since Russia's invasion, a small but growing number are heading in the other direction. At first they were foreign volunteers, Ukrainian expatriate men returning to fight and people delivering aid. Now, increasingly, women are also going back. 

Motivated by a desire to help loved ones in trouble, or to contribute to the defence and survival of their country and compatriots in ways large and small, these women are braving the bombs that have increasingly pounded Ukraine since Russian forces invaded on February 24. 

Many are not refugees but Ukrainian women who had been living and working abroad. Others had already chosen to stay put in their country but were forced to cross the border to shop for needed goods as supplies dried up under the onslaught at home. 

"I will go back and help. I am a health worker, so the hospitals need help," said Iryna Orel, 50, lugging her luggage as she boarded a train from Przemysl, Poland, to Lviv in western Ukraine. "And I will stay until the end." 

With Ukraine's government ordering men to stay and fight, the vast majority of people fleeing Ukraine have been women, children and the elderly. For those who can't or won't leave, the perils they face are many, and images such as those of a mortally wounded pregnant woman rushed on a stretcher from a maternity hospital in Mariupol testify to the dangers. 

Premature babies who were left behind by their parents lay in a bed in hospital number 3 in Mariupol, Ukraine, Tuesday, March 15, 2022. photo / AP 

Still, some women have chosen to head back toward the gunfire and bloodshed to contribute in whatever way they can. 

Reached by phone after arriving in the port city of Odesa, which has so far remained under Ukrainian government control, Orel said she was frightened at first by the air raid sirens and sounds of explosives, but "sitting and shaking with fear does not help." 

She envisions her role as providing medical care, but other women might choose to help defend the country militarily, she said. 

"Women can fight," she said. "Many women are patriotic to defend Ukraine — why not?" 

Women rushing into war zones or taking part in war efforts is nothing new. Female soldiers were a visible part of the Ukrainian military before the war, including in combat roles. Some women, like many men, are taking up arms for the first time. Plus, gender equality in the workplace as well as the military has traditionally been more common in post-Soviet states like Ukraine than many other parts of the world. 

Since the invasion, Polish border guards have tallied over 195,000 crossings of people from Poland to Ukraine, more than four in five Ukrainian nationals, spokeswoman Anna Michalska said Tuesday. That includes people who come and return — to buy food and other supplies in Poland and go back, or who bring relatives across and return. So some people are counted a number of times. 

A woman joins a queue to board a train leaving for Lviv in Ukraine at the train station in Przemysl, Poland. Photo / AP 

Poland has taken in more than 1.8 million refugees — over 60 per cent of the total exodus of three million people since the invasion, according to U.N. agencies. The UN refugee agency had initially predicted some four million refugees would flee — a figure that may soon be eclipsed. 

"What to say, really? Three million refugees in the space of just over two weeks. This is frightening and it doesn't stop," the UN High Commissioner for Refugees, Filippo Grandi, said in an interview in the Afghan capital, Kabul, where he was visiting to assure Afghans that despite the horrors of the war raging in Ukraine they have not been forgotten. 

"Everybody's asking how many refugees will come out of Ukraine," he said. "The answer is very simple: I simply don't know." 

Aid deliveries are making their way into Ukraine, as well as reported flows of weapons and fighters ready to use them. The International Committee for the Red Cross said 200 tons of medical supplies and relief items had arrived in the country, including water, mattresses, blankets, food, first aid kits, plastic tarps and more than 5000 body bags. 

Less noticed has been the entry or cross-border shuttling of women who are either trying to bring help or stay in the country to continue their lives as best they can. 

"I am returning to Ukraine to help people evacuate," said Maria Khalica, who lives in Italy and was headed to the Ukrainian capital, Kyiv. "I am in a more stable state now than my friends, who are under rocket attacks and bombs." 

"I know that Kyiv is also going to be occupied and we are taking the last chance to help other people" there, Khalica said, adding that she believes Russian forces will eventually seize the capital. 

Some women are returning to join their families and others to help in any way they can, either as health workers or with the army. 

"We plan to return to the family and we will decide with the family what to do next" said Olga Simanova, 56, who traveled from Germany to return to her family's hometown of Vinnycja. 

Meanwhile, the number of those fleeing continues to grow. 

James Elder, a spokesman for UNICEF, said some 1.4 million children have fled Ukraine since the invasion — or about 73,000 per day on average. 

That, he said, amounts to "55 every minute. So we are almost — since war started on the 24th of February — (at a point where) a child has become a refugee out of Ukraine every second." 

They have fled to countries across Eastern Europe: Romania has taken in more than 450,000, Moldova more than 337,000, Hungary over 263,000 and Slovakia some 213,000, according to the latest UNHCR tally on Tuesday. The Polish capital of Warsaw, alone, has taken in about 300,000 refugees, about a 15 per cent increase of its population of more than 1.7 million. 

"These are enormous numbers," said Moldovan Foreign Minister Nicu Popescu, who signed a 10 million-euro ($11 million) agreement with Italy on Tuesday to help with the refugee crisis. "The number of refugees represents 4 per cent of the whole Moldovan population."