Peace talks between U.S. and Russian delegations aimed at ending the war in Ukraine are underway Monday in Saudi Arabia, according to media reports. 

The discussions come after Ukrainian President Volodymyr Zelenskyy said a delegation from his country had a "quite useful" meeting with an American team in Riyadh on Sunday. 

"Our team is working in a fully constructive manner, and the discussion is quite useful. The work of delegations continues. But no matter what we’re discussing with our partners right now, Putin must be pushed to issue a real order to stop the strikes – because the one who brought this war must be the one to take it back," Zelenskyy said. 

The U.S. delegation meeting with the Russians on Monday is led by Andrew Peek, a senior director at the White House National Security Council, and Michael Anton, the director of the policy planning staff at the State Department, Reuters reported. It added that the Russians are represented by Grigory Karasin, the leader of the Russian upper house of parliament’s Foreign Affairs Committee, and Sergei Beseda, an adviser to the director of Russia’s Federal Security Service. 

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The delegations will focus on a ceasefire in the Black Sea, according to a report by Russia’s state-run TASS news agency, citing U.S. National Security Advisor Mike Waltz. In the next stage of the talks, the two sides will discuss "issues related to the verification of the ceasefire, the peacekeeping contingent, as well as the ownership of territories." 

President Donald Trump's Special Envoy Steve Witkoff told Fox News he doesn't believe Russian President Vladimir Putin wants to invade Europe. 

"Now I've been asked my opinion about what President Putin's motives are on a larger scale. And I simply have said that I just don't see that he wants to take all of Europe," Witkoff said during an appearance on "Fox News Sunday."

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"This is a much different situation than it was in World War II. There was no NATO," he added. "I take him at his word in this sense."

"I think you're going to see in Saudi Arabia on Monday some real progress, particularly as it affects a Black Sea ceasefire on ships between both countries. And from that you'll naturally gravitate to a full-on shooting ceasefire," Witkoff also said Sunday. 

Russia launched a massive drone attack targeting Kyiv and other major cities in Ukraine overnight on Sunday, highlighting just how far there is to go before a peace agreement can be made. 

Fox News’ Anders Hagstrom contributed to this report.