Russia is withdrawing a motorised infantry battalion from a region near Ukraine's eastern border, a Russian Defence Ministry spokesperson was quoted as saying by state news agencies this afternoon.
They did not make clear whether other Russian troops near the border would pull back.
US Secretary of State John Kerry said at talks yesterday with Russian Foreign Minister Sergei Lavrov that progress on resolving the crisis over Ukraine depended on a troop pullback from the border.
Mr Kerry said both sides were committed to finding a diplomatic solution.
Mr Lavrov said there would be co-operation with the interim Ukrainian government.
"Both sides made suggestions of ways to de-escalate the security and political situation in and around Ukraine," Mr Kerry said after meeting Mr Lavrov for four hours in Paris.
"Any real progress in Ukraine must include a pullback of the very large Russian force that is currently massing along Ukraine's borders.
"We believe these forces are creating a climate of fear and intimidation in Ukraine. It certainly does not create the climate that we need."
The Russian move into Crimea, following the removal of Ukraine's pro-Russia president in February, has sparked the worst East-West confrontation since the Cold War ended two decades ago.
While there were no outlines of an agreement, the two sides agreed to keep talking and both said the Ukrainian government had to be part of the solution.
"Neither Russia, nor the United States, nor anyone else can impose any specific plans on Ukrainians," Mr Lavrov told a separate briefing as quoted by the RIA news agency.
The US is adamant that there could be "no decisions about Ukraine without Ukraine", Mr Kerry told reporters, adding the US saw its role as creating conditions for negotiations between Russia and Ukraine.
Mr Kerry made clear that the US still considered Russian actions in Crimea to be "illegal and illegitimate".
The US and European Union have issued two rounds of sanctions on Russia, including visa bans and asset freezes on some of Russian President Vladimir Putin's inner circle.
Crimeans voted to secede from Ukraine and join Russia in a referendum on 16 March, which was dismissed as a sham by Western governments that say it violated Ukraine's constitution and was held only after Russian forces seized control of the region.
"The US and Russia have differences of opinion about events that led to this crisis, but both of us recognise the importance of finding a diplomatic solution and simultaneously meeting the needs of the Ukrainian people," Mr Kerry said.
US officials are deeply worried about the massing of what they estimate are up to 40,000 Russian troops on Ukraine's border, which is stoking concern in the US and elsewhere that Russia is preparing a wider incursion into Ukraine.
While Russia has said the build-up is part of normal Russian exercises, US President Barack Obama has described it as out of the ordinary that could be a precursor to other actions.
Mr Lavrov, speaking on Russian television on Saturday, said Russia had "no intention" of invading eastern Ukraine and reinforced a message from Mr Putin that Russia would settle, at least for now, for control over Crimea.
Mr Lavrov added, however that Russia was ready to protect the rights of Russian speakers, referring to what it sees as threats to the lives of compatriots in eastern Ukraine.
Meanwhile, Russian Prime Minister Dmitry Medvedev is visiting Crimea today with several members of his government.
It is the highest level visit to the Black Sea peninsula since its annexation by Russia earlier this month.
"[I'm] in Simferopol," Mr Medvedev said on Twitter after his plane landed in the main city in the region.
"Today the government will discuss the development of Crimea here," Mr Medvedev said.
He said Russia will make Crimea a special economic zone with tax breaks to attract investors.
"Our aim is to make the peninsula as attractive as possible to investors, so that it can generate sufficient income for its own development," Mr Medvedev said.
The Ukrainian foreign ministry said the visit is a "crude violation of the rules of the international community".