A second meeting between representatives of Russia and the United States is planned for the next two weeks, the RIA state news agency reported, citing Russian Deputy Foreign Minister Sergei Ryabkov.
Russia and the US held their first talks on ending the nearly three-year war in Ukraine on Tuesday, aimed at restoring relations and preparing to conclude the conflict.
The meeting will take place in a third country and the specific location is being agreed upon, Mr Ryabkov told RIA in an interview, without naming who would attend from the Russian or US sides.
Mr Ryabkov said there was "principled agreement" on both sides to hold consultations to work out "the entire block of so-called irritants."
"There is also an understanding that the round at the deputy level will be preceded by a consultative contact of the directors of the relevant departments. And their meeting may take place in the range of the next two weeks," he said.
The Kremlin said this week that a face-to-face meeting between President Vladimir Putin and US President Donald Trump was possible this month. Both men have said they want to meet.
Earlier, the United States proposed a United Nations resolution on the Ukraine conflict that omitted any mention of Kyiv's territory occupied by Russia, diplomatic sources said.
Washington's proposal comes amid an intensifying feud between Mr Trump and President Volodymyr Zelensky which has seen Mr Trump claim it was "not important" for his Ukrainian counterpart to be involved in peace talks.
It also appeared to rival a separate draft resolution produced by Ukraine and its European allies, countries that Mr Trump has also sought to sideline from talks on the future of the three-year-old war.
The Ukrainian-European text stresses the need to redouble diplomatic efforts to end the war this year, noting several initiatives to that end, while also blaming Russia for the invasion and committing to Kyiv's "territorial integrity".
The text also repeats the UN General Assembly's previous demands for an immediate and unconditional withdrawal of Russian troops from Ukraine.
Those votes had wide support, with around 140 of the 193 member states voting in favour.
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Washington's text, seen by AFP, calls for a "swift end to the conflict" without mentioning Kyiv's territorial integrity, and was welcomed by Moscow's ambassador to the UN Vassily Nebenzia as "a good move" - but stressed that it did not address the "roots" of the conflict.
In a break with past resolutions proposed and supported by Washington, the latest draft, produced ahead of a General Assembly meeting Monday to coincide with the third anniversary of the war, does not criticise Moscow.
Instead, the 65-word text begins by "mourning the tragic loss of life throughout the Russia-Ukraine conflict".
It then continued by "reiterating" that the United Nation's purpose is the maintenance of "international peace and security" - without singling out Moscow as the source of the conflict.
France's ambassador to the UN, Nicolas De Riviere, the EU's only permanent member of the council, said he had no comment "for the moment".
"A stripped-down text of this type that does not condemn Russian aggression or explicitly reference Ukraine's territorial integrity looks like a betrayal of Kyiv and a jab at the EU, but also a show of disdain for core principles of international law," said Richard Gowan of the International Crisis Group.
"I think even a lot of states that favor an early end to the war will worry that the US is ignoring core elements of the UN Charter."
