Vladimir Putin also praised the launch of a dialogue between Ukraine's government and its opponents even as fighting continued in parts of the country ahead of Sunday's presidential election.
The seemingly conciliatory approach suggested that Putin may believe he has achieved his key goal of maintaining Russian influence over eastern Ukraine without having to send in troops.
Russia still wants guarantees that Ukraine will not join NATO and will conduct constitutional reforms to give broader powers to its regions, something that would allow Moscow to maintain its clout in the Russian-speaking east that forms the industrial heartland. The continued unrest in the east is serving Putin by making it difficult for the government in Kiev to consolidate its control in the region.
Vladimir Putin specifically ordered Defense Minister Sergei Shoigu to pull back the forces involved in the ``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 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.
The Kremlin statement didn't say how many troops would be pulled out or specify how quick the withdrawal would be. NATO has estimated that Russia has 40,000 troops arrayed along the border with Ukraine.
The US and NATO said they saw no sign of a pullout after Putin's earlier claim of a withdrawal. On Monday, NATO Secretary General Anders Fogh Rasmussen reiterated that the military alliance has ``not seen any evidence at all that the Russians have started withdrawal of troops from the Ukrainian border.''
He said that NATO remains open to a political dialogue with Moscow and has proposed holding a meeting at the NATO-Russia Council next week.
In Washington, spokesmen for the White House and the Pentagon said U.S. officials have not yet seen any sign of a Russian troop pullback. Press secretary Jay Carney said if Russia had pulled its troops back, the U.S. would know and would be able to confirm it publicly.
Pavel Felgenhauer, an independent Moscow-based military analyst, said a pullout would be a sign that Putin has decided not to send troops to Ukraine, at least for now.
They think that the Ukrainian government won't be able to consolidate despite the presidential election, and the economic, political and social crisis will escalate,'' Felgenhauer said on Dozhd TV. ``They see no need to take the risky move of invasion, which would trigger serious sanctions.''
The US and the European Union have imposed travel bans and asset freezes on members of Putin's inner circle over Russia's annexation of Crimea. They have threatened to target entire sectors of the Russian economy with sanctions if Russia tries to derail Ukraine's election.
Ukraine is to vote on a successor to Kremlin-friendly President Viktor Yanukovych, who was ousted in February following months of protests in Kiev.
Ukraine's Foreign Ministry said it was checking the information about the troop withdrawal and urged Moscow also to cancel an air force exercise, set to take place in southwestern Russia from Wednesday to Sunday. It said the exercise _ which would involve more than 70 combat aircraft, including Tu-22M long-range bombers _ would fuel tensions during the vote.
Pro-Russia rebels, who have seized government buildings in eastern Ukraine and fought government troops, have declared two sprawling provinces independent and vowed to block the election. Ukraine and the West have accused Russia of fomenting the mutiny. Russia denies this.
Facing Western pressure, Putin supported a peace plan for settling the crisis, which was brokered by the Swiss chairmanship of the Organization for Security and Cooperation in Europe. Putin, who earlier had urged Ukraine to postpone the election, has now softened his stance.
The OSCE road map aims to halt the violence and de-escalate tensions by offering an amnesty for those involved in the unrest and urging talks on decentralization and the status of the Russian language. The OSCE also has sent an observer mission for the election.
The first round tables under the plan were held in Ukraine last week, but the government refused to invite representatives of the rebels in the east, whom it has dubbed ``separatists'' and ``terrorists.'' A third meeting is set for Wednesday.
Even though the Russian Foreign Ministry has criticized the round tables for failing to include the government's foes, Putin welcomed them as an attempt to establish dialogue. In a telephone conversation Monday with German Chancellor Angela Merkel, the two leaders expressed hope that the dialogue would continue, the Kremlin said.
Russian Foreign Minister Sergey Lavrov even sounded warmer regarding the round tables, calling them a ``step in the right direction.''
Vladimir Putin and Lavrov urged Ukrainian authorities to end immediately the military operation in eastern Ukraine, where fighting continued. Pro-Russia insurgents fired on a Ukrainian army checkpoint near a TV tower outside the city of Slovyansk, killing one soldier and wounding three, Ukraine's Defense Ministry said.
Associated Press journalists also witnessed mortar fire hitting the village of Andriyivka, just outside Slovyansk. While it was impossible to confirm who fired the mortars, they appeared to come from the Ukrainian government troops' positions. The shelling damaged a gas main running across a field and onto residents' lands. The pipeline caught fire, but no residents were hurt.
In Donetsk, the capital of one of the regions that pro-Russian insurgents declared independent last week, masked gunmen seized the office of the local branch of Ukrainian Railways and installed their man as its new chief. The company told the AP the attackers disrupted freight train traffic, stranding about 4,000 rail cars in the industrial region.
Amid the tensions, Kiev and Moscow traded accusations over two Russian journalists who were arrested Sunday by Ukrainian forces near Slovyansk.
The Ukrainian military said the two men, who had press accreditation with Life News, a Kremlin-connected TV channel, were with pro-Russian insurgents and were filming preparations for an attack outside Slovyansk. Russia has protested the arrest and asked the OSCE to assist in their release.
OSCE media freedom representative Dunja Mijatovic urged Ukraine to release the journalists and also condemned other recent cases of harassment of journalists by both sides in Ukraine.