Russian President Vladimir Putin has ordered a "partial withdrawal" of troops from the border with Ukraine, BBC quoted the German government as saying.
Putin informed Chancellor Angela Merkel of the move in a telephone conversation, her office said.
However, thousands of Russian troops are still said to be deployed along the border.
Earlier, Ukraine condemned a visit to Crimea by Russian Prime Minister Dmitry Medvedev and a delegation of government ministers.
Tensions between Russia and the West rose after the overthrow of pro-Kremlin Ukrainian President Viktor Yanukovych in February, following months of street protests.
Later, Russia's subsequent decision to annex Crimea triggered a crisis in relations.
Crimeans voted to leave Ukraine for Russia on 16 March, in a referendum condemned as illegal by the UN General Assembly.
