Top U.S. officials are leaving for Saudi Arabia for talks with Russian envoys on how to end the war in Ukraine, signaling that the Trump administration is eager to push for an agreement.

“We’re moving along,” President Trump told reporters in Florida on Sunday of the coming talks. “We’re trying to get peace with Russia, Ukraine, and we’re working very hard on it.”

Steve Witkoff , Trump’s Middle East envoy, confirmed that he was traveling Sunday with national security adviser Mike Waltz . Secretary of State Marco Rubio   is in Jerusalem and is scheduled to head to Saudi Arabia on Monday morning.

“I am going tonight,” Witkoff told Fox News’s “Sunday Morning Futures.” “I’ll be traveling there with the national security adviser, and we’ll be having meetings at the direction of the president, and hopefully we’ll make some really good progress.”

The arrangements for the U.S.-Russia meeting were firmed up following a Friday call between Rubio and Sergei Lavrov , the Russian foreign minister, which Moscow said was at the initiative of the Americans. The State Department said that the two diplomats had discussed “the opportunity to potentially work together on a number of other bilateral issues.”

The rapid push to convene U.S.-Russian talks followed a Wednesday call between Trump and Russian President Vladimir Putin .

Trump said the conversation led him to believe Putin wants a settlement. “We spoke long and hard,” Trump said. “Steve Witkoff was with him for a very extended period, like about three hours. I think [Putin] wants to stop fighting.”

Ukrainian President Volodymyr Zelensky has insisted that his country be involved in any talks about ending the war, which escalated following Russia’s February 2022 full-scale invasion of his country.

Zelensky said on NBC’s “Meet the Press” that Ukraine must be at the table and that it was important that European nations be represented as well.

“At the table, it’s very important to hear America, Europe, Ukraine, Russia,” he said.

The Trump administration’s Ukraine envoy, retired Lt. Gen. Keith Kellogg, said at a security conference in Munich Saturday that he didn’t foresee a direct role for European nations in the talks but that Ukraine would be at the negotiating table when formal peace talks are held.

Those comments alarmed European officials , who say that the outcome of the Ukraine war is a paramount concern for security on the continent.

Trump on Sunday said Zelensky would be involved in the talks, though he didn’t say at what stage, and insisted that both the Ukrainian and Russian leaders wanted to end the war.

“They want to end it fast, both of them, and Zelensky wants to end it too,” he said.

Speaking on “Fox News Sunday,” Waltz didn’t address the issue of Ukrainian involvement in the coming talks, but defended how the U.S. was proceeding. “They may not like some of the sequencing that is going on in these negotiations,” he said of European leaders, “but I have to push back on any notion that they aren’t being consulted—they absolutely are.”

French President Emmanuel Macron said Sunday that he would host an urgent meeting of European leaders on Monday to discuss the situation in Ukraine and European security. The meeting will include the leaders of Germany, Britain, Italy, Poland, Spain, the Netherlands and Denmark, as well as the Secretary-General of NATO, among others.

Write to Michael R. Gordon at michael.gordon@wsj.com , Maggie Severns at maggie.severns@wsj.com and Tarini Parti at tarini.parti@wsj.com