Russia proposed to Ukraine that the countries hold a second round of peace talks on Monday in Istanbul in order to exchange written proposals for a ceasefire and ending the war, Ukrainian and Russian officials said Thursday.

Vladimir Medinsky, the head of Russia's delegation at peace talks on Ukraine, said on Wednesday he had sent proposals to Ukraine with a date and venue to exchange memorandums, or conditions, to stop the fighting.

Moscow has proposed June 2 as the date for the next round of talks with Ukraine in Istanbul, Russian Foreign Minister Sergey Lavrov said during a press conference. In his remarks, Lavrov said the talks would be a continuation of the process launched during earlier negotiations on May 16 in Istanbul.

A leading security analyst has argued the likelihood of a ceasefire between Ukraine and Russia is growing increasingly slim, before encouraging United States President Donald Trump to hold his nerve and expand military support for the former as his relationship with Russia's President imploded into a public war of words.

Putin said efforts to end the war were "generally on the right track" and that Moscow was ready to work with Ukraine on a potential peace deal.

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The United States has received a draft proposal for implementing the ceasefire from Ukraine and is now waiting for the Russian version, US Special Representative for Ukraine, during remarks reported by Vedomosti on May 27.

The U.S. president lashed out at the Kremlin on Tuesday as the White House continued to consider increasing sanctions against Russia.