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Carlos Barria, Pool, Associated Press
Russia's President Vladimir Putin puts on an earphone during his meeting with China's President Xi Jinping, ahead of the Conference on Interaction and Confidence Building Measures (CICA) in Shanghai, China Tuesday, May 20, 2014.

MOSCOW — While unrest continued eastern Ukraine, Russian army units on Tuesday started dismantling their summer camps in the border regions in line with President Vladimir Putin's order, the Russian Defense Ministry said.

Russian forces in the Bryansk, Belgorod and Rostov regions are preparing for a march to their home bases, the defense ministry said. Putin ordered the retreat Monday, in a move appeared to be aimed at easing tensions with the West over Ukraine.

The U.S. and NATO, which estimates that Russia has 40,000 troops along the border with Ukraine, said Monday they saw no immediate sign of a pullout after Putin's claim.

Meanwhile, pro-Russian insurgents continued to exchange fire with government forces on the outskirts of the eastern city of Slovyansk while Ukraine's richest man, metals tycoon Rinat Akhmetov, toughened his stance against the rebellion.

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 hostages 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" Tuesday at the companies where they work by blowing sirens "in support of peace and against bloodshed."

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 in the country's eastern industrial heartland. The rebels declared the Donetsk and Luhansk regions independent following referendums earlier this month, which Ukraine and the West have denounced as a sham.

Alexander Zemlianichenko in Slovyansk, Ukraine contributed to this report.