Russian President Vladimir Putin has ordered troops near Ukraine's border to withdraw, the Kremlin said in an official statement today, adding that units in the Rostov, Belgorod and Bryansk regions should return to their permanent bases.
There is some scepticism about the announcement as Russia has made similar statements in the past, only for NATO to report no change on the ground. But correspondents say the removal of some 40,000 Russian troops near the Ukrainian border could help de-escalate the Ukraine crisis.
"In connection with the completion of the planned spring phase of military training ... at ranges in Rostov, Belgorod and Bryansk regions, Putin ordered the defence minister to withdraw the troops that took part in the exercises," the Kremlin statement said.
Meanwhile, heavy mortar fire outside Sloviansk apparently damaged a large gas pipeline and set off a fire this morning.
Tensions between Russia and the West rose after the overthrow of pro-Kremlin Ukrainian President Viktor Yanukovych in February, following months of street protests. Russia's subsequent annexation of Crimea escalated the crisis in relations.
Meanwhile clashes have continued between Ukrainian government forces and pro-Russia separatist militants in eastern Ukraine.
Russia called for an "immediate end to the punitive operation and violent actions" of Ukrainian government forces, demanding "the withdrawal of troops".
The BBC reports that people wondering if there is a command and control problem in the Russian military, as this is the third time that Russian units have been ordered to pull back to their bases from their positions on Ukraine's border.
There was supposedly a partial withdrawal at the end of March; but only one battalion moved. A full withdrawal was ordered in early May, but according to NATO officials the troops are still very much there. Now a withdrawal order has come from the Kremlin again.
The Kremlin statement said Putin "welcomes the first contacts between Kiev and the supporters of federalisation", even as one Ukrainian soldier was killed and one injured today in an attack by separatists on a checkpoint near Sloviansk, in the Donetsk region.
It comes as preparations continue for presidential elections in Ukraine on 25 May.
Pro-Russia separatists have taken control of government buildings across cities in south-eastern and southern Ukraine. Violence between the two sides has left dozens of people dead in recent weeks, but the rebels have not taken part in EU-brokered talks to defuse the crisis.
On Saturday, the separatists appointed a prime minister for what they call the People's Republic of Donetsk.