Russia and Ukraine will hold a third round of talks, likely on Monday, about ending hostilities.
David Arakhamia, a Ukrainian delegation member and the parliamentary faction leader of Ukrainian President Volodymyr Zelensky's party, confirmed in a social media post that new meetings will be held, but provided no details.
According to Interfax news agency, Russian negotiator Leonid Slutsky said, "The third round really could take place in the coming days, possibly on Monday."
Russia's TASS news agency quoted Slutsky as saying that in the second round, Ukraine had shown some openness to reaching an agreement.
Since Russia launched the "special military operation" against its neighbor on Feb 24, Ukrainian and Russian delegations have had two rounds of talks.
On Saturday, Ukraine said that the talks had not produced results, but that it would keep pursuing negotiations.
During a phone call with Turkish President Recep Tayyip Erdogan on Sunday, Putin said the suspension of the special operation to protect Donbass is possible only if Ukraine stops fighting and complies with Russian demands.
Putin confirmed Moscow's readiness for dialogue with Kyiv and its foreign partners, but he was aware of "Kyiv's attempts to delay the negotiations".
The Ukrainian delegation should show a more constructive approach at the new meeting, Putin stressed.
Russian Foreign Minister Sergey Lavrov said on Saturday that Zelensky's attempt to secure direct NATO assistance in the conflict was not helping the talks, but that Moscow was ready for a third round.
Zelensky criticized NATO on Saturday for ruling out a no-fly zone over Ukraine, but Putin spoke of "colossal and catastrophic consequences not only for Europe but also the whole world" if it were to be established.
"The current Ukrainian authorities must understand that if they continue to do what they are doing, they are putting in question the future of Ukrainian statehood," Putin warned on Saturday.
Russia and Ukraine agreed on Thursday on a cease-fire to open humanitarian corridors so civilians could leave areas of fighting, but it failed on Saturday amid fierce fighting in a number of cities.
Clashing reports emerged on Saturday regarding the death of a Ukrainian identified by media as a member of the country's negotiating team with Russia.
According to local media reports, Denis Kireev, who had been photographed participating in negotiations in Belarus in recent days, was killed by Ukrainian security forces during an attempt to arrest him.
Kireev, the reports said, had been suspected of treason.
A subsequent social media post by Ukraine's Defense Ministry confirmed Kireev's death but said he was an intelligence operative for Ukraine who died in the line of duty.