Ukrainian President Volodymyr Zelenskyy says peace talks with Russia now "sound more realistic", but time is still needed to secure a deal in Ukraine's interests.
A Ukrainian negotiator also sounded cautiously optimistic after the latest meeting, saying "there is certainly room for compromise" despite "fundamental contradictions".
It comes as a flurry of Russian attacks probed closer into central Kyiv on Tuesday, with a huge fire breaking out in a 15-storey apartment building in the west of the capital.
"Everyone should work, including our representatives, our delegation, for negotiations with the Russian Federation," Mr Zelenskyy said in his nightly address.
"It is difficult, but important, as any war ends with an agreement.
"The meetings continue, and, I am informed, the positions during the negotiations already sound more realistic. But time is still needed for the decisions to be in the interests of Ukraine."
Mr Zelenskyy has also hinted he may accept security guarantees that stop short of joining NATO.
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The leaders of Poland, Slovenia and Czech Republic arrived in Kyiv on Tuesday evening after taking a train to meet the president.
Polish President Mateusz Morawiecki tweeted a picture of the the group, saying: "Europe must understand that if it loses Ukraine it will never be the same again.
"It will no longer be Europe. Rather it will be a defeated, humiliated and pathetic version of its former self."
Europe must understand that if it loses Ukraine it will never be the same again. It will no longer be Europe. Rather it will be a defeated, humiliated and pathetic version of its former self. I want a strong and resolute Europe. pic.twitter.com/ENMRSDNuVU
— Mateusz Morawiecki (@MorawieckiM) March 15, 2022
It comes amid widespread condemnation of the death of an Irishman in Ukraine.
President Michael D Higgins said the death of journalist Pierre Zakrzewski in the Ukrainian capital was 'indiscriminate'.
The Fox News cameraman - who attended St Conleth's College in Dublin - was killed when his vehicle was hit by incoming fire.
Taoiseach Micheál Martin paid tribute to Mr Zakrzewski on Twitter, saying he was "Deeply disturbed and saddened by the killing of Irish citizen and journalist Pierre Zakrzewski and one of his colleagues today".
"My thoughts are with their families, friends and fellow journalists. We condemn this indiscriminate and immoral war by Russia on Ukraine."
Mr Zakrzewski is survived by his wife Michelle, his mother - who is French - and his five siblings. Two of his brothers and his mother still live in Ireland.
A curfew is in force in Kyiv until to 7.00am local time on Thursday, after a ratcheting up of strikes over the past 48 hours
Mayor Vitali Klitschko urged his fellow citizens to "spend the time in the bunkers" as he visited the aftermath of the latest attack in the Svyatoshynskyi district.
His brother Wladimir said: "It doesn't matter who you are on the Ukrainian soil now… if you have a press badge, or you're a little girl or boy, an adult, man or woman… or an old person… you are a target from Russia, from the Russian army."
In the southern city of Mariupol - which has been pummelled for several weeks - 20,000 people used 4,000 private cars to escape on Tuesday as a humanitarian corridor operated for a second day.
However, Ukrainian authorities have accused Russia of blocking aid supplies to the cut-off city.
Russian troops have also seized a hospital in Mariupol and taken around 500 people hostage, according to regional leader Pavlo Kyrylenko.
He said Russian forces had driven 400 people from neighbouring houses into Regional Intensive Care Hospital, where they joined around 100 doctors and patients inside.
The troops are using those inside the hospital as human shields and not allowing anyone to leave, he said on messaging app Telegram.
Another 8,533 people were also evacuated from the northeast Sumy region on Tuesday, according to Deputy Prime Minister Iryna Vereshchuk.
Meanwhile, Ukrainian forces pushed back an attempt to storm the second-biggest city of Kharkiv on Tuesday, said the head of the region.
Oleh Synehubov called it a "shameful defeat" and said the attackers were pushed back beyond their previous position in the Piatykhatky suburb.
Russia has met fierce resistance since the invasion began about three weeks ago and the number of soldiers killed means it is likely "struggling", according to the British Defence Ministry.
Latest Defence Intelligence update on the situation in Ukraine - 15 March 2022
Find out more about the UK government's response: https://t.co/sdQNbNojkk
— Ministry of Defence 🇬🇧 (@DefenceHQ) March 15, 2022
In its latest assessment, it said the Kremlin appears to be increasingly trying to replace lost soldiers to keep its plans on track.
"Russia is redeploying forces from as far afield as its Eastern Military District, Pacific Fleet and Armenia", it tweeted.
"It is also increasingly seeking to exploit irregular sources such as Private Military Companies, Syrian and other mercenaries.
"Russia will likely attempt to use these forces to hold captured territory and free up its combat power to renew stalled offensive operations," it added.
Additional reporting: IRN