WATCH: Zelenskyy meets with Trump in Florida to discuss end of Russia's war in Ukraine

PALM BEACH, Fla. (AP) — President Donald Trump on Sunday insisted Ukraine and Russia are "closer than ever before" to a peace deal as he hosted Ukrainian President Volodymyr Zelenskyy at his Florida resort, but he acknowledged that negotiations are complex and could still break down, leaving the war dragging on for years.

Watch Zelenskyy and Trump's remarks in the video player above.

The president's statements came after the two leaders met for a discussion that took place after what Trump described as an "excellent," two-and-a-half-hour phone conversation with Russian President Vladimir Putin, whose invasion of Ukraine launched the war nearly four years ago. Trump insisted he believed Putin still wants peace, even as Russia launched another round of attacks on Ukraine while Zelenskyy flew to the United States for the latest round of negotiations.

WATCH: What to know about the U.S.-Ukraine talks and proposal to end Russia's war

"Russia wants to see Ukraine succeed," Trump said during a late afternoon news conference following the meeting with Zelenskyy, whom he repeatedly praised as "brave."

Trump and Zelenskyy both acknowledged thorny issues remain, including whether Russia can keep Ukrainian territory it controls as well as security guarantees for Ukraine to ensure it's not invaded again in the future. After their discussion, they called a wide group of European leaders, including Ursula von der Leyen, president of the European Commission, and the leaders of Finland, France, Germany, Great Britain and Poland.

Zelenskyy thanked Trump for his work. "Ukraine is ready for peace," he said.

Trump and Putin will speak again

Trump said he'd follow the meeting with another call to Putin. Earlier Sunday, 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, Ukrainian authorities said. Explosions boomed across Kyiv as the attack began in the early morning and continued for hours.

READ MORE: Russia launches 'massive strike' on Kyiv, killing 1 and wounding many ahead of Ukraine-U.S. talks

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 noted that it was possible that the negotiations will fall apart.

"In a few weeks, we will know one way or the other, I think," Trump said. "We could have something where one item that you're not thinking about is a big item, breaks it up. Look, it's been a very difficult negotiation. Very detailed."

The face-to-face sit-down between Trump and Zelenskyy 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.

Kim reported from Washington and Morton from London. Associated Press writers Illia Novikov in Kyiv, Nicholas Riccardi in Denver and Darlene Superville in Washington contributed to this report.