Russia has said it is pulling back some of its troops from the Ukraine border after fears of an invasion were raised.
The defence ministry said some large scale drills would continue, but a number of units will return to their bases.
However, Ukraine has warned that it will need to see proof, saying: "when we see the withdrawal, then we'll believe the de-escalation".
The news comes as more than 100,000 Russian troops gathered on the border.
Russia has continuously denied any plan of attack.
In its statement, Russia's defence ministry said it was withdrawing some of the troops conducting exercises in military districts bordering Ukraine.
Defence ministry spokesman Igor Konashenkov said: "A number of combat training exercises, including drills, have been conducted as planned."
One such exercise that will continue is a large joint Russia-Belarus drill, due to end on February 20.
A British government source said it was waiting to see the scale of the withdrawal.
They said the pullout would need to be significant enough to make a difference to Russia's ability to invade to have any meaning.
However, the announcement has led to both Ukraine and Russia claiming victory in the stand-off.
Ukraine's Foreign Minister Dymytro Kuleba said: "We have managed together with our partners to deter Russia from any further escalation".
While a Russian foreign ministry spokeswoman, Maria Zakharova, said the day "will go into history as the day western war propaganda failed. They have been disgraced and destroyed without a single shot being fired."
The US has continued to warn that an invasion could come at any time as Russia seeks for Ukraine not to be allowed to join Nato.
Elsewhere in another development, the Russian parliament voted in favour of asking President Vladimir Putin to recognise the two self-declared republics of Luhansk and Donetsk in Eastern Ukraine as independent.
Russia has granted citizenship to at least 720,000 people in the two regions, the scene of an insurgency that began in 2014. If Mr Putin recognises the two breakaway regions, it will violate peace agreements.
