Donald Trump and Vladimir Putin hold talks in Alaska on Friday, with the U.S. president's hopes of sealing a ceasefire agreement on Ukraine uncertain but with a last gasp offer from Putin of a possible nuclear deal that could help both men save face.

The meeting of the Russian and U.S. leaders at a Cold War-era air force base in Alaska, their first face-to-face talks since Trump returned to the White House, comes amid Ukrainian and European fears that Trump might sell Kyiv out.

Trump, who once said he would end Russia's war in Ukraine within 24 hours, said on Thursday the three-and-a-half-year conflict had proven a tougher nut to crack than he had thought.

He said if his talks with Putin went well, setting up a subsequent three-way summit with Ukrainian President Volodymyr Zelenskyy - who was not invited to Friday’s meeting - would be even more important than his encounter with Putin.

Trump is pressing for a truce to bolster his credentials as a global peacemaker worthy of the Nobel Peace Prize, something he has made clear is important to him.

Ukraine and its European allies were heartened by their conference call on Wednesday in which, they said, Trump agreed Ukraine must be involved in any talks about ceding land. Zelenskyy said Trump had also supported the idea of security guarantees in a post-war settlement, although the U.S. president has made no public mention of them.

Wednesday's call eased their fears of a Trump-Putin deal that would leave Ukraine under pressure to make territorial and other concessions.

Putin, whose war economy is showing signs of strain, needs Trump to help Russia break out of its straitjacket of ever-tightening Western sanctions, or at the very least not to hit Moscow with more sanctions, something Trump has threatened.

The day before the summit, the Kremlin leader held out the prospect of something else he knows Trump wants - a new nuclear arms control agreement to replace the last surviving one, which is due to expire in February next year.

TRUMP SAYS PUTIN WILL DO A DEAL ON UKRAINE

Trump said on the eve of the summit that he thought Putin would do a deal on Ukraine, but he has blown hot and cold on the chances of a breakthrough. Putin, meanwhile, praised what he called "sincere efforts" by the U.S. to end the war.

A source close to the Kremlin told Reuters it looked as if the two sides had been able to find some unspecified common ground beforehand.

"Apparently, some terms will be agreed upon tomorrow (Friday) because Trump cannot be refused, and we are not in a position to refuse (due to sanctions pressure)," said the source, who spoke on condition of anonymity because of the matter's sensitivity.

Putin has set stringent conditions for a full ceasefire, but one compromise could be a phased truce in the air war, although both sides have accused the other of flouting a previous accord.

Analysts say Putin could try to look like he's giving Trump what he wants while remaining free to escalate in Ukraine if he wants to.

"If they (the Russians) are able to put a deal on the table that creates some kind of a ceasefire but that leaves Russia in control of those escalatory dynamics, does not create any kind of genuine deterrence on the ground or in the skies over Ukraine... that would be a wonderful outcome from Putin's perspective," said Sam Greene, director of Democratic Resilience at the Center for European Policy Analysis.

TRUMP SUGGESTS LAND TRANSFERS WILL BE NEEDED

Zelenskyy has accused Putin of bluffing and playing for time to avoid U.S. secondary sanctions and has ruled out handing Moscow any territory.

Trump has said land transfers between Russia and Ukraine could be a possible way of breaking the logjam.

Putin, whose forces control nearly one fifth of Ukraine, wants Trump to start reviving the two countries' shrunken economic, political and business ties and, ideally, not to make that process contingent on progress on Ukraine.

But it is unclear whether Putin is willing to compromise on Ukraine. In power for a quarter of a century, the Kremlin chief has staked his legacy on coming out of the war with something he can sell to his people as a victory.

Chief among his war aims is complete Russian control over the Donbas industrial region in eastern Ukraine, which comprises the Donetsk and Luhansk regions. Despite steady advances, around 25% of Donetsk remains beyond Russian control.

Putin also wants full control of Ukraine's Kherson and Zaporizhzhia regions; NATO membership to be taken off the table for Kyiv; and limits on the size of Ukraine's armed forces.

Ukraine has said these terms are unacceptable and tantamount to asking it to capitulate.

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