Representatives from the U.S., Ukraine and Russia on Friday held the first trilateral negotiations since Russia invaded Ukraine.
A White House official called the new talks "productive" and said they would continue into the weekend.
But officials downplayed the possibility of quickly arriving at any significant breakthroughs.
The nations' leaders are not attending the talks.
Ukraine sent military and intelligence officials, including the secretary of Ukraine's National Security Council.
Russia's delegation is made up entirely of military officials led by their military intelligence chief.
Representing the U.S. is special envoy Steve Witkoff and President Donald Trump' son-in-law Jared Kushner, as well as several military members from the Pentagon including Army Secretary Gen. Dan Driscoll and Supreme Allied Commander in Europe Gen. Alexus Grynkewich.
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Steve Witkoff on Thursday before he left for Moscow indicated some optimism about how talks were going, suggesting that they had "got it down to one issue" remaining for negotiation — disputes over who controls what territory if and when the conflict ends.
The Donetsk region in eastern Ukraine remains a central concern for Russia. Ukraine continues to fortify and maintain about a quarter of the territory there. Russia says that Ukraine must turn over all of that territory to bring an end to the fighting.
Russian officials have also indicated it will "continue to consistently pursue the objectives of the special military operation on the battlefield where the Russian armed forces hold strategic initiative until an engagement as or an agreement is reached."
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In a recent address, Ukraine's President Volodymyr Zelenskyy told Ukrainians that he'd monitored the negotiations. He said it's still too early to draw any conclusions from Friday's talks and that it's not just Ukraine who needs to show willingness to end this war, but also Russia.