MOSCOW (Reuters) -Russia has proposed holding the next round of direct talks with Ukraine in Istanbul on June 2 with a view to achieving a sustainable peace settlement, Russian Foreign Minister Sergei Lavrov said on Wednesday.

There was no immediate reaction from Kyiv.

Under pressure from U.S. President Donald Trump to end the bloodiest conflict in Europe since World War Two, delegates from the warring countries met earlier this month in Istanbul for the first time since March 2022, the month after Russia sent troops to its neighbour.

The May 16 talks failed to reach agreement on a ceasefire, as sought by Kyiv and its Western allies. Moscow said certain conditions must be met before such a move was possible.

"We hope that all those who are sincerely, and not just in words, interested in the success of the peace process will support holding a new round of direct Russian-Ukrainian negotiations in Istanbul," Lavrov said in a statement.

Russian President Vladimir Putin, after a call with Trump on May 19, said that Moscow was ready to work with Ukraine on a memorandum about a future peace accord.

Earlier on Wednesday, Vladimir Medinsky, the head of Russia's delegation at peace talks on Ukraine, said on the Telegram messaging app that he had called Ukraine's Defence Minister Rustem Umerov with proposals for the date and venue of the next meeting.

"Let me emphasise: right there, on the spot, we are ready to begin an essential, substantive discussion of each of the points of the package agreement on a possible ceasefire," he said.

Medinsky said he expected a reply from Ukraine.

Separately, Russian foreign ministry's spokeswoman Maria Zakharova said it was agreed that Russia and Ukraine would each prepare their vision of "modalities of settlement and ceasefire" and would discuss and exchange the documents at the next round of talks.

(Reporting by Vladimir Soldatkin and Maxim RodionovEditing by Gareth Jones)