US negotiators are holding talks in the Saudi capital Riyadh with their Ukrainian counterparts and separately with the Russians on Monday.
Washington's aim is to bring about an immediate partial ceasefire to the war in Ukraine, followed by a comprehensive peace deal.
So could these Riyadh talks produce the breakthrough so many are hoping for?
It depends who you listen to.
"I feel that he (Putin) wants peace," said President Trump's personal envoy Steve Witkoff, adding: "I think that you're going to see in Saudi Arabia on Monday some real progress."
Yet Dmitry Peskov, the Kremlin spokesman has dampened expectations. "We are only at the beginning of this path," he told Russian state TV.
Kyiv suffered one of its heaviest attacks from Russian drones on Saturday night, with three people killed, including a five-year-old girl.
"We need to push Putin to give a real order to stop the strikes," said Ukraine's President Volodymyr Zelensky in his evening address on Sunday. "The one who brought this war must take it away."
The Kremlin, meanwhile, seems to be in no rush to sign up to a ceasefire, with Vladimir Putin adding on numerous "nuances", or preconditions, before agreeing to the 30-day ceasefire proposed by Washington and agreed to by Kyiv.
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