There was initially no confirmation of a meeting as early as Thursday, from either Kiev or Washington.
Tuesday marks the fourth anniversary of Russia's full-scale invasion of Ukraine, which was ordered by Russian President Vladimir Putin.
After two meetings in Abu Dhabi in January and early February, representatives of Moscow, Kiev and Washington met in Geneva in mid-February.
Russia's negotiator Vladimir Medinsky described the talks afterwards as "difficult but business like".
There is no agreement in sight to end the war because Russia says its maximal demands are not being met.
Moscow is demanding that Kiev withdraw its troops from those parts of the Donbass that remain under Ukrainian control, which Ukrainian President Volodymyr Zelenskiy categorically rejects.
He sees no chance that the Ukrainian population would agree to ceding territory even in they were to vote on it.
Zelenskiy on Sunday described a pair of explosions in Lviv as a "cynical and brutal terrorist act" that was "organised by Russia".
Two explosions rocked the western Ukrainian city in the early hours, killing a 23-year-old policewoman and injuring 25 others.
"This was a terrorist attack," Lviv Mayor Andriy Sadovyi said in a video posted on his Telegram channel, adding that police have detained a female Ukrainian national.
Police said that the detained woman was a 33-year-old Ukrainian who had made and planted the bombs herself on behalf of Russian intelligence services.
Zelenskiy said the "perpetrators were recruited via Telegram".
"We have intelligence indicating that the Russians intend to continue carrying out such actions - in effect, attacks on Ukrainians," said the president.
"We must strengthen protection for our people."
Security forces had initially responded to a reported break-in at a shop near Lviv's old town.
Police said the first explosion went off shortly after midnight as they arrived, followed by a second blast just after reinforcements reached the scene.
The Lviv region is located in western Ukraine near the Polish border.
The region has become a refuge for many internally displaced people who fled the fighting in eastern Ukraine following Russia's full-scale invasion, which enters its fifth year on Tuesday.
At the same time, Lviv has repeatedly been targeted by Russian missile and drone strikes, underscoring that even areas far from the front lines remain vulnerable.
Russia carried out a further wave of airstrikes overnight, leaving one person dead and 15 injured.
Four children were hurt in the Kiev region while a 49-year-old was killed, the regional administration said.
"The main target of the attack was the energy supply, but normal residential buildings were also damaged, and there was damage to the railway," Zelenskiy said on X.
Russia attacked with almost 300 drones and 50 missiles and cruise missiles, Zelenskiy added.
In addition to Kiev, the areas of Dnipropetrovsk, Kirovohrad, Mykolaiv, Odessa, Poltava and Sumy were also affected.
"Moscow continues to invest more in attacks than in diplomacy," Zelenskiy said, referring to the negotiations between the warring parties, in which no peace is in sight so far.
This week alone, Russia deployed over 1300 combat drones, more than 1400 glide bombs and 96 rockets and cruise missiles, according to the president.
"That is why we must strengthen our air defence," Zelenskiy stressed, adding that that Ukraine needs systems that can respond to ballistic missiles.
"Each such package protects critical infrastructure and maintains normality of life."
