Russian President Vladimir Putin has ordered troops deployed near Ukraine to return to their home bases, while fighting continued in the eastern parts of the country.
Putin on Monday ordered Defence Minister Sergei Shoigu to pull back forces involved in "planned spring" drills in the Rostov, Belgorod and Bryansk regions to their home bases, the Kremlin said.
The order appears to go further than a similar statement by the Russian leader two weeks ago that troops were being pulled back from the border to shooting ranges.
The three regions border Ukraine and the withdrawal of troops deployed there to other Russian provinces could signal a genuine attempt by Moscow to de-escalate the worst crisis in its relations with the West since the Cold War.
It would also be a move that was easily verifiable by Western intelligence.
The West, however, said they saw no sign of a pullout after Putin's earlier claim of a withdrawal and NATO on Monday said it did not see any immediate movements to validate the latest assertions.
The Kremlin statement did not say how many troops would be pulled out from the three regions or specify how quick the withdrawal would be.
The United States and the European Union have placed travel bans and asset freezes on members of Putin's entourage since Russia's annexation of Crimea over what has been perceived as overly aggressive moves. The withdrawal of troops could ease these tensions.
The EU also threatened to target entire sectors of the Russian economy with sanctions if Russia tries to derail Ukraine's presidential vote due to take place on May 25.
Facing the prospect of more Western sanctions, Putin supported a peace plan for settling the crisis, which was brokered by the Swiss chairmanship of the Organisation for Security and Cooperation in Europe.
Pro-Russian rebels, who have seized government buildings in eastern Ukraine and fought government troops, however, vowed to block Sunday's vote, especially in the newly-declared independent regions of Donetsk and Luhansk
The OSCE road map, supported by Putin, aims to halt the violence and de-escalate tensions ahead of the vote, by offering an amnesty for those involved in the unrest and urging talks on decentralisation and the status of the Russian language.
The OSCE also has sent an observer mission for the election.
The first round tables under the plan were held in Ukraine last week, but the government refused to invite representatives of rebels in the east, whom it dubbed "separatists'' and "terrorists".
Even though the Russian Foreign Ministry has criticised the round tables for failing to include the government's foes, Putin welcomed them as an attempt to establish dialogue.
He also urged the Ukrainian authorities to immediately end a military operation in eastern Ukraine, where fighting continued on Monday.
Pro-Russian fighters fired on a Ukrainian army check-point near a television tower outside the eastern city of Slovyansk, killing one soldier and wounding three, Ukraine's defence ministry said.
Slovyansk has been the epicentre of fighting between Ukrainian troops and pro-Russian fighters, who have seized government buildings across the east.