As Ukraine says it has accepted a proposal for a 30-day ceasefire, US secretary of state Marco Rubio says “the ball is now in Russia’s court”.
Ukrainian President Volodymyr Zelenskyy said he accepted the proposal as his country, which has been fending off Russia’s full-scale invasion for the past three years, was “ready for peace”.
Here is what Sky News correspondents think of the latest developments in the ongoing efforts to end the hostilities.
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Ivor Bennett, Moscow correspondent
Will Russia accept a ceasefire? Hard to say.
Because throughout the past few weeks and months, Moscow has always said it doesn’t want a temporary truce.
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Instead, it’s called for a long-term peace deal that tackles what it sees as the “root causes” of the conflict.
In Moscow’s mind, “root causes” means Western aggression and NATO’s historical eastward expansion.
By making that a consistent criterion for peace, Russia has been trying to ensure that its own security concerns are met in the event of a final deal being signed.
I think it’s also a way of legitimising its full-scale invasion, which Russia claims was done to protect Russian speakers in eastern Ukraine as a result of the Minsk agreements not being upheld.
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The Minsk agreements were ceasefire deals signed between Kyiv and Russian-backed separatists in the Donbas in 2014 and 2015. Moscow’s reasoning is that Kyiv can’t be trusted to stick to a truce.
But this is largely posturing by the Kremlin, to reinforce its own narrative around the conflict – that it is the victim, fighting a defensive war.
A more compelling reason as to why Russia favours a permanent deal over a temporary one is because Ukrainian forces are on the back foot.
A pause in the fighting would give them time to regroup, so why would Moscow agree?
It wants to have Kyiv begging for mercy when it comes to the negotiating table, so that a permanent deal would be entirely in Russia’s favour.
The problem for Vladimir Putin, though, is that he now has to put his money where his mouth is.
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In order to win Donald Trump’s favour, the Kremlin has been relentless in trying to cast itself as the peacemaker and Ukraine as the warmonger.
It’s worked up until this point, with America increasingly siding with Russia. But now, all of a sudden, Kyiv is calling Moscow’s bluff.
James Matthews, US correspondent, in Washington DC
It looks like progress and it sounds like progress. How much it is actual progress will be a matter for the Russians.
Moscow will decide if this step forward amounts to two steps back.
The Americans and Ukrainians did the easy bit in Saudi Arabia. This was a diplomatic healing between both parties, a reset on relations that restores a military alliance.
Clearly, Ukraine will welcome the US lifting its pause on intelligence sharing and weapons supply.
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It will strengthen the ties between Washington and Kyiv, even if trust remains undermined.
There is deep suspicion in Kyiv surrounding the motivations of President Trump and his relationship with Mr Putin.
Ukrainian president Zelenskyy called the ceasefire proposal a positive step – he’s content as far as it goes, even if he’ll have questions around the context.
Ukraine was second behind Russia on the guest list for talks with the Americans and, while Mr Trump has courted Mr Putin, he’s cold-shouldered Mr Zelenskyy.
Discussions between Mr Trump and Mr Putin will surely have given the US president a guide on how the Russians will respond to offers made.
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Would Mr Trump have proposed a ceasefire without an assurance that Mr Putin would accept?
Unlikely, given everything Moscow has to gain.
The future floated for Ukraine by the Trump administration doesn’t include NATO membership, doesn’t reflect a desire to roll back Russian territorial gains and doesn’t rule out lifting sanctions against Moscow.
For Ukraine, there are difficult questions about what comes after the guns go silent.
A ceasefire in the current conditions isn’t the starting point that Mr Zelenskyy would have chosen but, realistically, it’s the only starting point he’s got.
Alex Rossi, international correspondent, in Jeddah, Saudi Arabia
It was a long day of negotiations but at the end it appeared that the Ukrainian and American delegations had found common ground. When they entered the talks they looked focused – there is a lot riding on the talks.
When they emerged after sundown it was clear that they had achieved something – small steps on what will be a long and difficult road to achieve any sort of peace.
The initial agreement saw progress on a readiness by the Ukrainians to accept an immediate interim 30-day ceasefire in theory.
Whilst there are still many outstanding issues, there is now movement to end a war that has been grinding on for more than three years.
For the Ukrainians, they wanted and needed to mend the relationship with the US after that now infamous diplomatic spat in the Oval Office.
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They were seeking a restoration of military aid and intelligence sharing. The US has now announced it will immediately restart its assistance.
What the Americans wanted to see was a Ukraine that was prepared to be flexible and make difficult decisions to reach a peace agreement.
The Ukrainians were clearly persuasive on that count and the US delegation sounded convinced.
But the war cannot stop without Russian agreement and whether Moscow bites and also agrees to an interim ceasefire is far from clear.
They have given mixed signals.
On the one hand, officials have said the Kremlin’s war objectives remain the same and there will be no concessions but they have also said they are waiting to hear the details of the talks.
Clearly the ball is now in Moscow’s court.
Mr Trump’s envoy Steve Witkoff is heading to Moscow later in the week.
It’s reported he will discuss the diplomatic proposals with Mr Putin.
But getting a lasting and sustainable peace will not be easy – Russia’s leader is unlikely to accept anything that does not allow him to present his “special military operation” as anything other than a total victory.
And until an agreement is reached, the violence and the killing will continue.