|Russia has said the troops deployed along its border with Ukraine are taking part in military exercises|
Mr Putin informed Chancellor Angela Merkel of the move in a telephone conversation, according to her office.
Thousands of Russian soldiers are still said to be deployed along the border.
Earlier, Ukraine condemned a visit to Crimea by Russia’s Prime Minister Dmitry Medvedev and a delegation of government ministers.
A foreign ministry spokesman in Kiev said the highest-level trip to the Black Sea peninsula by officials from Moscow since its annexation by Russia was a “crude violation” of international rules.
A note protesting against the presence of an official in “the territory of another state without preliminary agreement” had been sent, he added.
Crimeans voted to leave Ukraine for Russia on 16 March, in a referendum condemned as illegal by the UN General Assembly.
He also vowed to quickly boost salaries and pensions, and to improve education, healthcare and local infrastructure.
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 decision to annex Crimea triggered a crisis in relations.
The United States and the European Union have imposed sanctions on members of President Vladimir Putin’s inner circle and other officials. Russia has retaliated with its own sanctions on US lawmakers.
US Secretary of State John Kerry told his Russian counterpart, Sergei Lavrov, on Sunday that resolving the crisis depended on Russia pulling back its troops from along Ukraine’s border.
On Monday afternoon, Mr Putin informed Germany’s chancellor about “the partial withdrawal of Russian troops he ordered from the eastern border of Ukraine”, Mrs Merkel’s office said in a statement.
“On top of that, the two discussed further possible steps to stabilise the situation in Ukraine and Trans-Dniester,” it added, referring to a pro-Russian region bordering western Ukraine that proclaimed independence from Moldova in 1990.
A Kremlin statement did not mention a partial withdrawal, but said the two leaders had discussed “opportunities for international support for the restoration of stability” in Ukraine.
|Russian MPs voted to annul deals with Ukraine allowing Russia’s Black Sea Fleet to be based in Crimea|
|Ukraine’s interim President, Olexander Turchynov, meanwhile inspected members of its National Guard|
|Mr Turchynov said he hoped the newly-formed National Guard would become an “elite” force|
|Russian Prime Minister Dmitry Medvedev said Crimea’s development was a “state priority”
Mr Putin had also told Mrs Merkel that Ukraine had to enact constitutional reforms to ensure that the interests of all its regions were respected, and called for measures to end the “blockade” of Trans-Dniester, it added.
The Russian foreign ministry separately said that Mr Lavrov had followed up his meeting with Mr Kerry with a telephone conversation on Monday, in which they discussed “steps to help resolve the crisis situation”.
After an earlier meeting with his French and Polish counterparts, German Foreign Minister Frank-Walter Steinmeier said: “I hope we have overcome the worst escalation.”
His comments came after the Russian defence ministry announced that a 15th Separate Motor-Rifle Brigade battalion had completed field exercises at the Kadamovsky range in the Rostov region, and was returning to its permanent base in the Samara region.
A motor-rifle battalion is believed to comprise about 500 men.
Sources at Nato said there had been some indications of troop movements, but that it was hard to evaluate their significance at this stage, reports the BBC’s Jonathan Marcus in Brussels.
A senior Western diplomat said approximately 40,000 soldiers were in place, and that they still offered a huge potential for intimidation.
On Tuesday, Nato foreign ministers will meet in Brussels to discuss further steps to reassure allies and additional ways to help Ukraine.