Fresh talks between the US, Russia and Ukraine could take place "as early as next week", President Zelenskyy has said.
Negotiations took place in Abu Dhabi on Friday and Saturday, and were described as "productive" and "constructive" by Washington and Mr Zelenskyy respectively.
"The central focus of the discussions was the possible parameters for ending the war," President Zelenskyy wrote on X after the meeting.
More talks are expected in Abu Dhabi next Sunday, according to a US official who spoke anonymously to Reuters.
"We got to real granular detail and (we feel) that next Sunday will be, God willing, another meeting where we push this deal towards its final culmination," they said.
Sky correspondent Sally Lockwood said officials had reported "unexpected chemistry" between the two sides and that the atmosphere "surpassed expectations".
A UAE government spokesman suggested a meeting between Mr Zelenskyy, President Putin - and possibly President Trump - did not seem too far away.
Despite the positive reports, the talks didn't stop Moscow raining down hundreds of missiles and drones on Ukraine's two largest cities, Kyiv and Kharkiv, early on Saturday morning.
"This barbaric attack once again proves that Putin's place is not at [Donald Trump's] Board of Peace, but in the dock of the special tribunal," said Ukrainian foreign minister Andrii Sybiha.
Some 1.2 million buildings were left without power nationwide, while temperatures plummeted to -13C (8.6F) in the capital.
Military analyst Professor Michael Clarke said the strikes were timed to influence the talks by attempting to convince the White House that the Russian army was unstoppable.
One person was killed in the attack and 31 people were injured. Footage showed firefighters scrambling to tackle flames ignited by the strikes.
Unexpected chemistry raises hopes of Putin-Zelenskyy meeting
When the second day of talks ended in the UAE late on Saturday afternoon, there was a sense the negotiations may have broken down — or, at best, reached a deadlock.
But more detail has since emerged from US officials about what happened behind closed doors. The Russian and Ukrainian delegations were described as "respectful" — and even had lunch together.
According to officials briefed on the talks, the atmosphere between these sworn enemies surpassed expectations. It was described as positive, with the two sides showing unexpected chemistry as they worked to find solutions.
It's a jarring contrast to developments overnight, when Ukraine's two largest cities were hit by a barrage of missiles and drones.
A maternity hospital and a shelter for displaced people were among the buildings struck, while around a million Ukrainians are without power after attacks on energy infrastructure.
"There’s been a lot of carnage. A lot of killing. But there was respect," one US official said during a press briefing organised by the White House.
We now know the Americans have been working to arrange this meeting for the past six weeks.
A meeting between Donald Trump and President Zelenskyy in Davos is said to have helped set the stage for the talks in Abu Dhabi. US officials say both Zelenskyy and Vladimir Putin were sufficiently encouraged by the progress to send negotiating teams to the UAE.
Not only are all three parties expected to return to Abu Dhabi next Sunday to resume talks, but the idea of a bilateral meeting between presidents Zelenskyy and Putin is said to be "very close".
US officials say we could soon see delegations meeting in Russia — or even Russians travelling to Kyiv.
"Targeting civilians and civilian infrastructure is a clear breach of the rules of warfare," UN human rights chief Volker Turk said.
Despite images showing damage to apartments, the Russian defence ministry claimed it targeted Ukrainian military and industrial installations as well as energy and transport infrastructure used by the armed forces.
The Ukrainian negotiating team's main task in Abu Dhabi was to convey how relentless Russian strikes were undermining diplomacy, Mr Zelenskyy said.
For its part, the Kremlin continued to demand Mr Zelenskyy give up all the land Russian soldiers have occupied by force, plus the rest of the eastern Donbas region.
Ukraine shows little appetite to concede - and nor do its citizens, according to polls.
Russia even floated the idea of using the bulk of nearly $5bn (£3.66bn) in Russian assets frozen in the US to fund rebuilding the cities it has destroyed in the Donbas.
Mr Zelenskyy dismissed it as "nonsense".
Curated by Marcus Thompson
