President Vladimir Putin has said he ordered Russian troops to pull out from the regions near Ukraine to help create a positive environment for the nation's presidential vote.
But Mr Putin added that it would be hard for the Kremlin to deal with its winner because of continuing fighting in eastern Ukraine.
The pullout announced on Monday was meant to create "favourable conditions for Ukraine's presidential vote and end speculations", Mr Putin told reporters in Shanghai, China, where he attended a security summit.
Referring to comments by the US and Nato that they are not seeing any sign of the withdrawal, Mr Putin said that "those who aren't seeing it should look better". He said the pullout will be clearly visible in satellite images, according to Russian news agencies.
Mr Putin's pullout order and his statement welcoming the election, which he had previously urged to postpone, has shown that he has no immediate intention to send the Russian army into Ukraine, where pro-Russian insurgents have seized government buildings and clashed with Ukrainian government forces in weeks of fighting that has left dozens dead.
Mr Putin's moves reflected an apparent desire to ease tensions with the West over Ukraine and avoid further sanctions.
But the Russian leader said today that it would have made more sense for the Ukrainian authorities to have a constitutional referendum that would approve a new constitution before the election.
"It will be very difficult for us to develop relations with people who come to power amid a punitive operation in south-eastern Ukraine," he said.
Mr Putin added that Russia has helped establish a dialogue between the central government in Kiev and people in the south east.
"We have done everything to help start these contacts," he said.
The Russian defence ministry said that its military units in the regions near Ukraine today began moving to railway stations and airfields en route to their home bases, which they are expected to reach before June 1.
Yet Nato, which estimates that Russia has 40,000 troops along the border with Ukraine, repeated today it could not yet see any signs of a Russian pullout.
Russian television broadcast footage of columns of tanks and howitzers towed by heavy trucks. It was not immediately clear where the footage was taken.
The ministry said its units will make most of the journey by air or rail to reduce the pressure on highways.
General Vladimir Shamanov, the chief of the Russian airborne forces, said in televised remarks that battalions from three airborne divisions would return to their home bases within 10 days.
The Ukrainian government and the West have seen the Russian military build-up in the areas near the border as a possible precursor for grabbing more land following Russia's annexation of Crimea in March. The United States and the European Union slapped sanctions on members of Mr Putin's entourage after Russia took Crimea, and have threatened more crippling sanctions if Moscow tries to invade eastern Ukraine or derail its presidential vote set for this Sunday.
Meanwhile, clashes between the rebels and Ukrainian government forces continued today in eastern Ukraine. The insurgents have faced a challenge from Ukraine's richest man, metals tycoon Rinat Akhmetov, who demanded an end to the mutiny which he said was destroying eastern Ukraine and called on workers to hold protests. They have also faced angry local residents, increasingly exasperated over being caught in crossfire that have destroyed their housing and endangered their lives.