French President Emmanuel Macron has told reporters that President Vladimir Putin assured him that Russian forces would not ramp up the crisis near Ukraine's borders, reports BBC.
"I secured an assurance there would be no deterioration or escalation," he said before meeting Ukraine's leader.
However, Russia said any suggestion of a guarantee was "not right".
Russia has denied any plans to invade Ukraine, but it has assembled more than 100,000 troops near its borders.
US officials believe Russia has assembled 70% of military forces needed for a full-scale invasion.
The tensions between Russia, Ukraine and the West come nearly eight years after Russia annexed Ukraine's southern Crimea peninsula.
Moscow accuses the Ukrainian government of failing to implement the Minsk agreement - an international deal sponsored by Germany and France to restore peace to the east, where Russian-backed rebels control swathes of territory and at least 14,000 people have been killed since 2014.
Putin asked to show 'concrete steps'
President Macron this week is on a diplomatic tour of national capitals. He arrived in the Ukrainian capital, Kyiv, on Tuesday after almost six hours of talks with Mr Putin in Moscow on Monday.
At a news conference with Ukraine's President Volodymyr Zelensky, Mr Macron said there was now the chance to "make these negotiations move forward" between Russia and Ukraine, and that he could see "concrete solutions" to reducing tensions.
Mr Zelensky meanwhile called on Mr Putin to take serious measures to reduce tensions. "I do not really trust words, I believe that every politician can be transparent by taking concrete steps," he said.
Mr Putin hinted on Monday that some of Mr Macron's proposals "could form the basis of further joint steps" - although they were "probably still too early to talk about".
A French official later told reporters that the two leaders had agreed that Russia would pull troops out of Belarus at the end of exercises taking place near Ukraine's northern borders.
Kremlin spokesman Dmitry Peskov however denied any deal had occurred - although the troops were expected to return to Russia at some point, he said.
President Macron's diplomatic push later moved to Berlin for a meeting with the German chancellor, Olaf Scholz, and Polish President Andrzej Duda.
US President Joe Biden met the German leader in Washington on Monday and threatened to shut down a key Russian gas pipeline to Germany, called Nord Stream 2, if Moscow invaded Ukraine.
Chancellor Scholz - on his first trip to Washington since becoming chancellor and facing criticism for his response to the Ukraine crisis - was however more ambiguous about the pipeline than Mr Biden.
Writing in The Times newspaper on Tuesday, UK Prime Minister Boris Johnson said the UK was considering deploying Royal Air Force fighters and Royal Navy warships "to protect south-eastern Europe".
Western countries have already rejected a number of Moscow's demands, including that the Nato defence alliance rule out Ukraine becoming a member, and that it reduce its military presence in eastern Europe.