In a subsequent briefing with Ukrainian President Volodymyr Zelensky, a source familiar with the discussion quoted Trump as saying the Russian leader had offered to freeze most of the front lines if Kiev forces surrendered all of Donetsk, an industrial region that is one of Moscow's main targets.

Zelensky rejected the request, the source said. Russia already controls a fifth of Ukraine, including about three-quarters of the Donetsk region, which it first entered in 2014.

Trump also said he agreed with Putin that a peace deal should be sought without a first ceasefire, which Ukraine and its European allies, so far supported by the US, have demanded.

Zelensky said he would meet Trump in Washington on Monday, while Kiev's European allies welcomed Trump's efforts but vowed to support Ukraine and tighten sanctions on Russia. The source said that European leaders were also invited to attend those talks.

Trump's meeting with Putin in Alaska on Friday, the first US-Russia summit since Moscow launched an all-out invasion of Ukraine in February 2022, lasted just three hours.

"Everyone has decided that the best way to end the terrible war between Russia and Ukraine is to go directly to a peace agreement, which would end the war, and not just to a cease-fire agreement, which often does not achieve results," Trump announced on the Truth Social social network.

His mixed comments about the meeting largely matched the public views of Moscow, which says it wants a full settlement - not a break - but that it will be complex because the positions are"diametrically opposed".

Russia has been gradually advancing for months. The war - Europe's deadliest in 80 years - has killed or wounded more than a million people on both sides, including thousands of mostly Ukrainian civilians, according to analysts.

Before the summit, Trump said he would not be happy unless a ceasefire was agreed. But later he said that, after the conversation with Zelensky on Monday,"if everything goes well, we will schedule a meeting with President Putin."

Those conversations will bring back memories of a meeting in the Oval Office of the White House in February, where Trump and Vice President J.J. D. Vance publicly brutally criticized Zelenski.

Zelensky said that he is ready to meet with Putin.

But Putin has not signaled any progress in Russia's long-standing demands, which include a veto on NATO membership, and has not publicly mentioned the meeting with Zelensky. His aide, Yuriy Ushakov, said that the tripartite summit was not discussed.

In an interview with Fox News' Sean Hannity, Trump signaled that he and Putin had discussed the transfer of territory and security guarantees for Ukraine and that they had"generally agreed."

"I think we're pretty close to an agreement," he said, adding:"Ukraine has to agree to it. Maybe they'll say 'no'."

When asked what he would advise Zelensky to do, Trump said:"We have to make a deal."

"Look, Russia is a very big power and they are not," he added.

Necessary security guarantees for Ukraine

Zelensky has consistently said he cannot hand over territory without changes to the Ukrainian constitution, and Kiev sees Donetsk"fortress cities" like Slavyansk and Kramatorsk as a bulwark against Russian advances in more regions.

Zelensky also insisted on security guarantees to deter Russia from invading again in the future. He said he and Trump discussed"positive signals from the U.S. side" about involvement and that Ukraine needs lasting peace, not"just another break" between Russian invasions.

Italian Prime Minister Giorgio Meloni said the most interesting development concerned security guarantees - inspired by Article 5 of NATO.

"The starting point of the proposal is to define a collective security clause that would allow Ukraine to benefit from the support of all its partners, including the US, ready to take action in case it is attacked again," she said.

Putin, who has so far opposed the involvement of foreign ground forces, said he agreed with Trump that Ukraine's security must be"secured."

"I hope that the understanding we have reached will allow us to get closer to that goal and pave the way for peace in Ukraine," Putin said at a briefing where neither leader answered questions.

"We expect that Kiev and European capitals... will not try to derail the progress that is emerging..."

For Putin, the very fact that he was sitting with Trump was a victory. He has been ostracized by Western leaders since the start of the war, and just a week earlier he faced the threat of new sanctions from Trump.