President Donald Trump said Sunday he believes both Ukrainian President Volodymyr Zelenskyy and Russian President Vladimir Putin truly want peace, as he welcomed the "brave" Ukrainian leader for talks at his Florida resort.

"The two leaders want it to end," Trump said at the outset of the meeting at Mar-a-Lago. Before Zelenskyy arrived, Trump spoke with Putin by phone for more than an hour, and planned to speak with him again soon after.

Greeting Zelenskyy at Mar-a-Lago, Trump said of him: "This gentleman has worked very hard, and is very brave, and his people are very brave."

Zelenskyy, by Trump`s side, said he`d discuss issues of territorial concessions with Trump, which have so far been a red line for his country. He said his negotiators and Trump`s "have discussed how to move step by step and bring peace closer" and would continue to do so in the meeting.

Russia intensified its attacks on Ukraine`s capital in the days before the meeting.

Putin`s foreign affairs adviser Yuri Ushakov, said the Trump-Putin call was initiated by the U.S. side, lasted over an hour, and was "friendly, benevolent, and businesslike." Ushakov said Trump and Putin agreed to speak again "promptly" after Trump`s meeting with Zelenskyy.

But Ushakov added that a "bold, responsible, political decision is needed from Kyiv" on the fiercely contested Donbas region in eastern Ukraine and other matters in dispute for there to be a "complete cessation" of hostilities.

In overnight developments, three guided aerial bombs launched by Russia struck private homes in the eastern city of Sloviansk, according to the head of the local military administration, Vadym Lakh. Three people were injured and one man died, Lakh said in a post on the Telegram messenger app.

The strike came the day after Russia attacked Ukraine`s capital with ballistic missiles and drones on Saturday, killing at least one person and wounding 27, a day before planned talks between the leaders of Ukraine and the United States, Ukrainian authorities said. Explosions boomed across Kyiv as the attack began in the early morning and continued for hours. Trump said, however, that he still believes Putin is "very serious" about ending the war.

"I believe Ukraine has made some very strong attacks also," Trump told reporters as Zelenskyy stood by his side. "And I don`t say that negatively. I think, you probably have to. I don`t say that negatively. But I think, he hasn`t told me that, but there have been some explosions in various parts of Russia. It looks to me, like, I don`t know. I don`t think it came from the Congo."

Trump and Putin will speak again

Trump said he`d call Putin after the meeting with Zelenskyy and also reach out to European leaders who he said "have been really great." He tempered his optimism about ending the conflict, however.

"It`ll either end or it`s going to go on for a long time and millions of additional people will be killed," Trump said.

Trump and Zelenskyy sitting down face-to-face underscored the apparent progress made by Trump`s top negotiators in recent weeks as the sides traded draft peace plans and continued to shape a proposal to end the fighting. Zelenskyy told reporters Friday that the 20-point draft proposal negotiators have discussed is "about 90% ready" - echoing a figure, and the optimism, that U.S. officials conveyed when Trump`s chief negotiators met with Zelenskyy in Berlin earlier this month.

During the recent talks, the U.S. agreed to offer certain security guarantees to Ukraine similar to those offered to other members of NATO. The proposal came as Zelenskyy said he was prepared to drop his country`s bid to join the security alliance if Ukraine received NATO-like protection that would be designed to safeguard it against future Russian attacks.

‘Intensive` weeks ahead

Zelenskyy also spoke on Christmas Day with U.S. special envoy Steve Witkoff and Jared Kushner, Trump`s son-in-law. The Ukrainian leader said they discussed "certain substantive details" and cautioned "there is still work to be done on sensitive issues" and "the weeks ahead may also be intensive."

The U.S. president has been working to end the war in Ukraine for much of his first year back in office, showing irritation with both Zelenskyy and Putin while publicly acknowledging the difficulty of ending the conflict. Long gone are the days when, as a candidate in 2024, he boasted that he could resolve the fighting in a day.

After hosting Zelenskyy at the White House in October, Trump demanded that both Russia and Ukraine halt fighting and "stop at the battle line," implying that Moscow should be able to keep the territory it has seized from Ukraine.

Zelenskyy said last week that he would be willing to withdraw troops from Ukraine`s eastern industrial heartland as part of a plan to end the war, if Russia also pulls back and the area becomes a demilitarized zone monitored by international forces.

Putin wants Russian gains kept, and more

Putin has publicly said he wants all the areas in four key regions that have been captured by his forces, as well as the Crimean Peninsula, illegally annexed in 2014, to be recognized as Russian territory. He also has insisted that Ukraine withdraw from some areas in eastern Ukraine that Moscow`s forces haven`t captured. Kyiv has publicly rejected all those demands.

The Kremlin also wants Ukraine to abandon its bid to join NATO. It warned that it wouldn`t accept the deployment of any troops from members of the military alliance and would view them as a "legitimate target."

Putin also has said Ukraine must limit the size of its army and give official status to the Russian language, demands he has made from the outset of the conflict.

Putin`s foreign affairs adviser, Yuri Ushakov, told the business daily Kommersant this month that Russian police and national guard would stay in parts of Donetsk - one of the two major areas, along with Luhansk, that make up the Donbas region - even if they become a demilitarized zone under a prospective peace plan.

Ushakov cautioned that trying to reach a compromise could take a long time. He said U.S. proposals that took into account Russian demands had been "worsened" by alterations proposed by Ukraine and its European allies.

Trump has been somewhat receptive to Putin`s demands, making the case that the Russian president can be persuaded to end the war if Kyiv agrees to cede Ukrainian land in the Donbas region and if Western powers offer economic incentives to bring Russia back into the global economy.