US presidential envoy Steve Witkoff is to visit Moscow this week, the White House has confirmed, in what would be his fourth trip to Russia since Trump took office.
The reports said the proposal was first raised at a similar meeting with European nations in Paris last week. Trump has since threatened to “take a pass” on efforts to end the conflict unless progress is made quickly.
Ukraine will be represented by President Volodymyr Zelensky's chief of staff, Andriy Yermak, Foreign Minister Andriy Sybiga and Defence Minister Rustem Umerov.
Russia resumed air strikes on Ukraine this week following a brief Easter truce.
The Kremlin has warned that it cannot rush into a ceasefire deal.
Ukrainian authorities also reported strikes in the regions of Kyiv, Kharkiv, Poltava and Odesa.
Trump promised on the campaign trail to strike a deal between Moscow and Kyiv in 24 hours but has since failed to secure concessions from Russian President Vladimir Putin to halt his troops in Ukraine.
US, French and British foreign ministers, along with a senior German official, met in Paris last Thursday to discuss events.
Rubio and Trump have warned since the Paris talks that the United States could walk away from peace talks unless it saw quick progress.
Trump “wants to see this war end, and he wants to stop the killing on both sides of this war, and he’s been very clear about that for quite some time, and he has grown frustrated with both sides of this war, and he’s made that very known”, his spokeswoman Karoline Leavitt said on Tuesday.
Wednesday's Ukraine negotiations are less high-level than last week's Paris talks.
Trump proposed an unconditional ceasefire in March, the principle of which was accepted by Kyiv but rejected by Putin.
French Foreign Minister Jean-Noel Barrot hailed the Paris talks as a breakthrough because the United States, Ukraine, and European ministers had “gathered around the same table” when Europe had previously feared it would be excluded from decision-making.
European leaders are also scrambling to work out how to support Ukraine should Trump pull Washington's vital military and financial backing.
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