The trip was a Polish idea, after the EU warned of potential security risks.
The leaders decided to go by train because flying by Polish military jet could have been viewed by Russia as dangerously provocative, BBC Europe editor Katya Adler reported. It was not immediately clear when their train would make the return trip to Warsaw.
Poland’s Mateusz Morawiecki said history was being made in Ukraine’s capital.
“It is here, that freedom fights against the world of tyranny. It is here that the future of us all hangs in the balance,” he tweeted. Mr Morawiecki added that Ukraine could count on the help of its friends.
The prime ministers sat down for a briefing with their Ukrainian counterpart Denis Shmyhal, and President Volodymyr Zelensky, who thanked them for the “powerful” gesture of support.
They were accompanied to Ukraine by Jaroslaw Kaczynski, the leader of Poland’s ruling Law and Justice party.
Sepsis and hunger as civilians hide
Russian artillery and warplanes are continuing to pound cities and towns across Ukraine.
In Mariupol, a key port city in the south-east, hundreds of people crammed into the basement of a large public building are running out of food, with many also in need of urgent medical help, the news Hugo Bachega was told.
“Some have developed sepsis from shrapnel in the body,” said Anastasiya Ponomareva, a 39-year-old teacher who fled the city at the start of the war but is in contact with friends there. “Things are very serious.”
Her friends are with other families who spend most of their day in the basement. From time to time they go upstairs for sunlight, but rarely outside. They have all left homes that are no longer safe or no longer standing.
At an intensive care hospital on the western outskirts of the city, staff described being treated like hostages by Russian forces.
One employee was quoted as saying that Russian troops had “forced 400 people from neighbouring houses to come to our hospital,” adding: “We can’t leave.”
The regional governor, Pavlo Kyrylenko, said the facility had been all but destroyed by shelling in recent days, but that staff had continued to treat patients in the basement.
Separately, about 2,000 cars were able to leave Mariupol along a humanitarian evacuation route, according to city authorities. Before the war around 400,000 people lived in the city, which has endured intense bombardment by Russian forces. The city council says well over 2,000 civilians have died.
Cameraman and journalist killed in Kyiv
A cameraman and a journalist working for Fox News were killed when their vehicle was struck by incoming fire on the outskirts of the Ukrainian capital Kyiv, staff at the US network said.
Fox News chief executive Suzanne Scott described the deaths of Pierre Zakrzewski, 55, and Oleksandra Kuvshinova, 24, as “heart-breaking”.
Their colleague, 39-year-old Benjamin Hall, was also wounded in the incident and taken to hospital.
The attack followed the death on Sunday of 50-year-old US journalist Brent Renaud, who was shot and killed in the Ukrainian town of Irpin.
Missing anti-war TV journalist reappears
The Russian journalist who protested against the war in Ukraine on a live TV news programme and shared a video describing the invasion as a crime was fined 30,000 roubles (£214; $280) and released.
Marina Ovsyannikova, an editor at state-controlled Channel One, was detained on Monday after she ran onto the set holding a sign saying “no war”. But concerns were later raised over her safety after reports that she could not be contacted.
On Tuesday, however, she appeared at a court hearing.
Ms Ovsyannikova told reporters afterwards that she had gone two days with no sleep, had been questioned for over 14 hours, and was not given access to legal help.
Russians agree to bring US astronaut back to Earth
Fears that US astronaut Mark Vande Hei – who has been in space for 355 days – might lose his lift back to Earth on board a Russian capsule were thankfully put to bed when it was confirmed he would indeed be making the trip home.
The American, and two other Russian cosmonauts, will be brought back, landing in Kazakhstan.
Joel Montalbano, Nasa’s ISS programme manager, said: “I can tell you for sure Mark is coming home… We are in communication with our Russian colleagues. There’s no fuzz on that.”
Biden barred from entering Russia
Meanwhile, as Western nations impose further sanctions on Russia, Moscow retaliated on Tuesday by slapping sanctions on US President Joe Biden and 12 other US officials.
The list includes Secretary of State Antony Blinken, Defence Secretary Lloyd Austin, press secretary Jen Psaki and other members of the administration.
But there were also a couple of surprises on the list: former Secretary of State Hillary Clinton and Mr Biden’s son, Hunter.
The measures block their entry into Russia and freeze any assets held in the country.
