The premier specifically ordered defence minister Sergei Shoigu to pull back forces involved in “planned spring drills” in the Rostov, Belgorod and Bryansk regions to their home bases, the Kremlin said.
The order appears to go further than a similar statement by the Russian leader two weeks ago that troops were being pulled back from the border to shooting ranges.
The three regions border Ukraine and the withdrawal of troops deployed there to other Russian provinces would signal a genuine attempt by Moscow to de-escalate the worst crisis in its relations with the West since the Cold War. It also would be easily verifiable by western intelligence.
However, western nations said they saw no sign of a pull-out after Mr Putin’s earlier claim of a withdrawal, and Nato said yesterday it did not see any immediate movements to validate the latest assertions.
The Kremlin did not say how many troops would be pulled out from the three regions, nor did it give a timescale.
The United States and the European Union have issued travel bans and asset freezes against people with close links to the Kremlin and Mr Putin over Russia’s annexation of Crimea.
They have also threatened to target entire sectors of the Russian economy with sanctions if Russia tries to derail Ukraine’s presidential vote, set for Sunday.
Russia has already seen a flight from investors in recent months.
Pro-Russian rebels, who have seized official buildings in eastern Ukraine and fought government troops, have already declared two sprawling provinces independent and vowed to block Sunday’s vote.
Facing the prospect of more western sanctions, Mr Putin supported a peace plan for settling the crisis, which was brokered by the Swiss chairmanship of the Organisation for Security and Co-operation in Europe (OSCE).
The OSCE road map aims to halt the violence and de-escalate tensions ahead of the vote by offering an amnesty for those involved in the unrest and urging talks on decentralisation and the status of the Russian language. The OSCE has also sent an observer mission for the election.
The first round-table talks under the plan were held in Ukraine last week, but the government refused to invite representatives of rebels in the east, whom it has dubbed “separatists” and “terrorists”.
Even though the Russian foreign ministry has criticised the round-table discussions for failing to include the government’s foes, Mr Putin has welcomed them as an attempt to establish dialogue.
He also urged the Ukrainian authorities to immediately end a military operation in eastern Ukraine, where fighting continued yesterday.
Pro-Russian insurgents fired on a Ukrainian army check-point near a television tower outside the eastern city of Slovyansk, killing one soldier and wounding three, Ukraine’s defence ministry said.
Journalists also witnessed mortar fire hitting the village of Andriyivka, just outside Slovyansk.
The shelling damaged a gas main running across a field and on to local residents’ land. The pipeline caught fire, but no residents were hurt.