It is the second time Mr Putin has said Russian forces are being pulled back, with the Russian President announcing on May 7 that they had been "withdrawn".

Mr Putin said: "We're always being told that our forces on the Ukrainian border are a concern. We have withdrawn them."

Vladimir Putin has ordered troops to return to base, says the Kremlin

Russia has about 40,000 troops near the border with eastern Ukraine, close to where Ukraine's security forces and separatists have been engaged in low-level conflict.

A senior NATO military officer told Reuters: "We haven't seen any movement to validate (the report)."

Mr Putin reiterated Russia's demand that Kiev end what the Kremlin called a "punitive operation" against the separatists.

Meanwhile, Russian Foreign Minister Sergei Lavrov told another Russian newsagency RIA that Russia's relations with the EU and NATO needed "rethinking" as a result of the crisis in Ukraine.

Russian soldiers in Crimea

Several towns and cities in east Ukraine have come under the control of separatists, who are seeking independence from Kiev.

Referendums held across two Ukrainian regions of Donetsk and Luhansk, declared illegal by the West and Kiev, voted by a huge majority to break away from the rest of the country.

Many have criticised the vote however, saying it was not organised in a way that provided for a fair and representative result.

Russia's refusal to condemn the separatists' actions led last week to the EU imposing further sanctions on key Russians and others supportive of Ukraine's breakaway regions.