WASHINGTON (Kyodo) -- Senior U.S. and Russian officials on Tuesday could not set a meeting between their presidents but agreed to continue talks toward ending the war in Ukraine.

U.S. Secretary of State Marco Rubio agreed with his Russian counterpart Sergey Lavrov during talks in Saudi Arabia that both sides will form high-level teams to begin working on a path to ending the conflict "in a way that is enduring, sustainable and acceptable to all sides," according to the State Department.

It was the first meeting between the top diplomats of Russia and the United States on ending the war in Ukraine since Moscow launched its full-scale invasion nearly three years ago.

Hours after the talks, U.S. President Donald Trump told reporters at his Mar-a-Lago estate in Florida that he is now "much more confident" of a deal.

"They were very good. Russia wants to do something. They want to stop the savage barbarianism," he said, adding he wants to first aim for a cease-fire before achieving peace.

But no Ukrainian officials were part of the meeting. Ukraine's President Volodymyr Zelenskyy has voiced strong opposition to any peace negotiations without his country's participation and warned that Trump is only trying to achieve a cease-fire.

Referring to complaints from Ukraine and European allies that they were being sidelined from the ongoing process between the United States and Russia, Trump derided them for failing to do better before his involvement.

"I think I have the power to end this war, and I think it's going very well," he said, adding that Ukraine should hold an election, given that Zelenskyy's five-year term was supposed to be through May 2024.

Trump asserted that forcing Zelenskyy to stand for reelection is not coming from Russia but from the U.S. president and "many other countries."

"It's been a long time since we've had an election. That's not a Russia thing," he said, noting that Ukraine is being "just wiped out."

The Riyadh meeting, which lasted about four and a half hours, came after Trump and Russian President Vladimir Putin held phone talks last week and agreed to begin negotiations "immediately" toward ending the war.

Following the phone conversation on Wednesday, Trump suggested he would hold an in-person meeting with Putin possibly in Saudi Arabia, without saying when, and expressed his hope for a "cease-fire in the not-too-distant future."

According to the State Department, in a bid to normalize the workings of their diplomatic missions, Rubio agreed with Lavrov on the establishment of a consultation mechanism to deal with "irritants" to the U.S.-Russia relationship.

Rubio, who led a U.S. delegation that included national security aide Michael Waltz and special envoy Steve Witkoff, also agreed with the Russian foreign minister to lay the groundwork for cooperation on matters of mutual geopolitical interest and economic opportunities, the department said.