* Updates with Zelenskiy comments, EU official, details
* Czech, Polish, Slovenian leaders head to Kyiv
* Zelenskiy aide says war over by May
* Apartment in capital hit by shells
* Russia calls TV news broadcast protest "hooliganism"
By Pavel Polityuk, Natalia Zinets and Omer Berberoglu
LVIV, Ukraine/KYIV, March 15 (Reuters) - Three European prime ministers headed to Kyiv by train on Tuesday for the first visit of its kind since war began, even as buildings there were ablaze and rescue workers were trying to pull survivors from the rubble of fresh Russian bombardment.
That foreign leaders could attempt to visit the Ukrainian capital was a striking symbol of Ukraine's success so far in fending off an assault that Western countries believe was aimed at seizing Kyiv weeks ago.
"It is our duty to be where history is forged. Because it's not about us, but about the future of our children who deserve to live in a world free from tyranny," said Polish Prime Minister Mateusz Morawiecki, who crossed the border with Czech Prime Minister Petr Fiala and Janez Jansa of Slovenia.
Fiala said the aim was "to confirm the unequivocal support of the entire European Union for the sovereignty and independence of Ukraine."
The visit comes at a time when Ukrainian officials are playing up the hope the war could end sooner than expected, saying Moscow may be coming to terms with its failure to impose a new government on Kyiv by force.
In the latest hint at compromise, President Volodymyr Zelenskiy said on Tuesday Kyiv was prepared to accept security guarantees that stop short of its long-term objective of the NATO alliance membership, which Moscow opposes.
Ukraine understands it does not have an open door to join NATO yet, Zelenskiy said in a video message: "If we cannot enter through open doors, then we must cooperate with the associations with which we can, which will help us, protect us ... and have separate guarantees."
Peace talks between Russian and Ukrainian delegations via a video link restarted on Tuesday after a pause on Monday, the first time a round of talks ran to a second day.
Kremlin spokesperson Dmitry Peskov said it was too early to predict progress: "The work is difficult, and in the current situation the very fact that (the talks) are continuing is probably positive."
The European leaders will arrive in a city still under bombardment, where around half of the 3.4 million population has fled and residents spend nights sheltering in underground stations.
Two powerful explosions rocked Kyiv before dawn on Tuesday and tracer fire lit up the night sky. A high-rise apartment building was in flames in the morning after being struck by artillery.
Firefighters tried to douse the blaze and rescue workers helped evacuate residents trapped inside using mobile ladders. Officials said four people had died in Russian shelling of the capital in the early hours.
Sitting on the ground outside, resident Igor Krupa said he survived because he had slept under a makeshift shelter of furniture and metal weights: "All the windows went out and all the debris went into the apartment."
But despite reducing some cities to rubble, Europe's biggest invasion force since World War Two has been halted at the gates of Kyiv, and Russia has failed to capture any of Ukraine's 10 biggest cities.
In his most confident public statement yet, Zelenskiy called on Russian troops to surrender.
"You will not take anything from Ukraine. You will take lives," he said. "But why should you die? What for? I know that you want to survive."
Czech and Polish officials said the prime ministers' mission was coordinated with the EU and agreed by the bloc's leaders at a summit last week. However, some officials in Brussels were circumspect.
While every peace initiative was welcome, the trip "poses serious security risks," noted one EU official. "Some leaders might also wonder: will this jeopardise or will this improve conditions for negotiations with the Russians. It remains to be seen, of course. It's a fine line."
One of Zelenskiy's top aides said the war would be over by May, or even end within weeks, as Russia had run out of fresh troops.
"We are at a fork in the road now," Oleksiy Arestovich said in a video. He said he expected either a peace deal within one or two weeks or another Russian attempt with new reinforcements, which could prolong the conflict for another month.
"I think that no later than in May, early May, we should have a peace agreement, maybe much earlier: we will see," Arestovich said.
In Rivne in western Ukraine, officials said 19 people had been killed in a Russian air strike on a TV tower. If confirmed it would be the worst attack on a civilian target so far in the northwest where Russian ground troops have yet to tread.
Peace talks have focused so far on local ceasefires to let civilians evacuate and bring aid to surrounded cities.
Worst-hit is the southeastern port of Mariupol, where hundreds have been killed since Russia laid siege in the war's first week. Russian troops let a first column of cars leave Mariupol on Monday but attempts to bring in aid convoys have failed for 10 straight days. Ukrainian officials said they would try again.
While Russia has failed to seize any cities in the north and east, its has had more success in the south, where Moscow said on Tuesday it now controlled the entire Kherson region.
In an intelligence update on Tuesday, Britain's ministry of defence reported demonstrations against Russian occupation in the southern cities of Kherson, Berdyansk and Melitopol.
The war has brought economic isolation upon Russia and led to a near total crackdown on free speech there, with all major independent media shut and Western social media apps switched off.
An employee of the main state TV channel stood behind an anchor during a news broadcast late on Monday and held up an anti-war sign.
She was quickly arrested. Kremlin spokesperson Peskov called her protest "hooliganism".
The United Nations says nearly 3 million people have fled Ukraine since the start of the war.
Tanya, who crossed the Danube River to Romania, said she had fled the southern frontline town of Mykolaiv to save her child. "Because the people that are there now are Russians, Russian soldiers, and they kill children."
(Reporting by Reuters bureaus; Writing by Peter Graff; Editing by Tomasz Janowski)