-Russia and Ukraine will hold a third round of talks on Monday about ending hostilities, Ukrainian negotiator David Arakhamia said in a Facebook post on Saturday, without providing further details.
The Russian side was less definitive, saying merely that the talks might start on Monday.
Delegations from Ukraine and Russia have had two rounds of talks since Russia launched a full-scale invasion of its neighbour on Feb. 24.
On Thursday, the sides agreed to open humanitarian corridors to allow civilians out of some combat zones, although there have been delays in implementing them.
Ukraine said on Saturday the talks had not produced results but that it would keep pursuing negotiations.
"The third round of talks will take place on Monday," Arakhamia, who is also the parliamentary faction leader of Ukrainian President Volodymyr Zelenskiy's party, wrote.
Russian news agency Interfax later quoted Russian negotiator Leonid Slutsky as saying "the third round really could take place in the coming days, it's possible it will be on Monday."
Russian Foreign Minister Sergei Lavrov said on Saturday that Zelenskiy's attempt to secure direct NATO help in the conflict between their countries was not helping talks between the two sides, but that Moscow was ready for a third round.
Wary of being dragged into Moscow's war on its neighbor, NATO on Friday turned down Zelenskiy's appeal to create a no-fly zone over Ukraine, prompting the Ukrainian president to say that the alliance had given Russia the green light to continue its bombing campaign.
Earlier on Saturday, Ukrainian Foreign Minister Dmytro Kuleba said he was open to talks with Lavrov, but only if they were "meaningful."
The Kremlin said on Friday that progress in the negotiations would depend on Kyiv's reaction to Moscow's position on how to end the war, which had been conveyed to Ukraine on Thursday.
Russia's TASS news agency quoted Slutsky as saying the Ukrainian side had shown some openness in the second round to reaching an agreement.