The European Commission welcomed Moscow's announcement and said its monitors in Ukraine would verify the current situation.
On January 1, Russia cut off all shipments to Ukraine after the two countries failed to renew a gas agreement for 2009 and Moscow accused Kiev of stealing gas destined to its European clients.
Ukraine, an ex-Soviet state with pro-Western leaders, has also angered the Kremlin in the past months because of its attempts to join Nato.
The dispute damaged the reputation of both countries as reliable energy partners and prompted Europe to search once again for alternative energy sources and routes.
Russia supplies an average of 350 million cubic metres of gas to the 27-nation block during the winter season.
The European Union relies on Russia for about one quarter of all the natural gas it needs, and 80 per cent of those volumes arrives via pipelines crossing Ukraine.