Yekaterina Len, 61, cries outside her ruined house following a shelling in Sloviansk, eastern Ukraine, on Tuesday. Sloviansk has been the major battleground of militia forces and Ukrainian government troops in eastern Ukraine. Alexander Zemlianichenko / Associated Press

Russia's Defense Ministry said on Monday its military units close to the border with Ukraine have started dismantling their camps in preparation for returning to their permanent bases, in line with an order from President Vladimir Putin.

A day after Putin issued a pullout order in an apparent bid to ease tensions with the West over Ukraine, the Russian Defense Ministry said that its forces in the Bryansk, Belgorod and Rostov regions were preparing for the journey to their home bases.

However, NATO spokeswoman Oana Lungescu challenged the Russians "to prove that they are doing what they are saying."

NATO, which estimates that Russia has 40,000 troops along the border with Ukraine, said it is watching the situation closely but could not yet confirm any changes.

The Russian Defense Ministry said on Tuesday it would take time for troops to dismantle their camps and load equipment on trucks for a march to railway stations. It did not say how many troops were being pulled out from the three regions or how long it would take.

Putin's order made it clear that he has no immediate intention to send the Russian army into eastern Ukraine, where militia forces have seized government buildings and clashed with Ukrainian government forces in weeks of fighting that has left dozens dead.

On Tuesday, the rebels continued to exchange fire with government forces on the outskirts of the eastern city of Sloviansk, which has been the epicenter of the still ongoing clashes.

'Warning protest'

Ukraine's richest man, metals tycoon Rinat Akhmetov, toughened his stance against the rebellion, saying it has devastated the eastern regions that form the nation's industrial heartland.

In a statement, Akhmetov called for an end to the mutiny in the east, which he described as a "fight against the citizens of our region".

"Is looting in cities and taking peaceful citizens hostage a fight for the happiness of our region? No, it is not!" Akhmetov said.

He called on all workers in the region to hold a "peaceful warning protest" on Tuesday at the companies where they work by blowing sirens "in support of peace and against bloodshed" and continue such actions in the following days.

Russia has scathingly criticized the new Ukrainian authorities, who came to power in February after the toppling of a pro-Russian president, for using the military against the rebellion. The rebels declared the Donetsk and Lughansk regions independent following referendums earlier this month, which Ukraine and the West have denounced as a sham.

However, Putin's order to withdraw troops from areas near the border and his support for Ukraine's presidential vote this Sunday, which he had previously sought to postpone, appeared to reflect a desire to de-escalate the crisis and avoid further Western sanctions.