Vladislav Surkov, the assistant of Russian President Vladimir Putin, and Kurt Walker, Washington's special representative for Ukraine, held their third meeting in Belgrade yesterday to discuss the matter, according to Russian media, quoted by the website Sputnik Serbia.
"It is not surprising that the United States and Russian Federation have different concepts of how to make peace, but we will continue to work to get there", the statement said.
Fighting between Kyiv government forces and Russia-backed separatists who hold parts of Ukraine's Donetsk and Luhansk regions has killed more than 10,000 people since April 2014.
Neither side revealed details of the talks in Belgrade, which took place just days after the Wall Street Journal reported that Washington was preparing to propose the deployment of 20,000 global peacekeepers to Ukraine. "Our American friends presented their proposals concerning our Security Council draft resolution, which contained 29 paragraphs".
This was the third meeting between the Russian and United States representatives held in 2017. "Our delegation came to the conclusion that three of them were acceptable", the Kremlin aide added.
Both Surkov and Volker were confident that "the Minsk Agreements should be implemented".
While US president Donald Trump - dogged by allegations over his links to Moscow - rarely mentions Ukraine in public, Mr Volker and other officials in Washington have given Kiev strong backing in its undeclared war with Russian Federation.
Secretary of State Rex Tillerson during which they "coordinated further steps for the deployment of an global United Nations mission" in the separatist-held parts of Luhansk and Donetsk, including the border between those areas and Russian Federation, which Kyiv says is used to ship weapons and military personnel in from Russian Federation.
Volker said Washington wants the mission to monitor the entire conflict area and make sure heavy weapons are pulled back. Volker had refused to meet with Surkov in Russian Federation, and Surkov is barred from the European Union under sanctions imposed in response to Russia's aggression against Ukraine. Surkov and Volker earlier held talks in the Belarusian capital of Minsk on August 21 and in the Serbian capital of Belgrade on October 7.
Belgrade is a neutral venue.
Tillerson appointed Volker, a former USA ambassador to North Atlantic Treaty Organisation, as the US special representative for Ukraine negotiations in July.
A statement said that Mitchell will also meet business and civic leaders to discuss Ukrainian efforts to transform the country into a "prosperous, secure, and democratic European state".