SLOVYANSK, Ukraine -- Pro-Russia separatists fighting government forces in eastern Ukraine faced a surge of local anger Tuesday and a new challenge from the country's richest man, who demanded an end to their rebellion.

Metals tycoon Rinat Akhmetov, riding a wave of public dismay with the fighting, issued a strong call against the mutiny in the east, which he described as a "fight against the citizens of our region" that has devastated Ukraine's industrial heartland.

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

The tycoon vowed to challenge the insurgents who declared independence last week in the eastern regions of Donetsk and Luhansk, an area of 6.5 million people.

"No one will frighten us, including those calling themselves a Donetsk People's Republic," he said.

Akhmetov had initially taken a noncommittal stance as the mutiny engulfed the east, drawing criticism from the authorities in Kiev. But last week, his company organized citizen patrols of steelworkers who worked alongside police in the Black Sea port of Mariupol to improve security. The move forced insurgents to vacate the government buildings they had seized in the key southeastern city.

The tycoon urged all workers in eastern Ukraine to hold peaceful protests at their companies by blowing sirens Tuesday "in support of peace and against bloodshed." He suggested they keep up those protests in the coming days.

It was unclear if his call had a broad following.

Interior Minister Arsen Avakov quickly hailed Akhmetov's move, saying on Facebook that "the people's power and energy will sweep the terrorist scum away better than any counterterrorist operation."

One of the leaders of rebels in Donetsk, Denis Pushilin, retaliated Tuesday by threatening to nationalize Akhmetov's assets over his refusal to pay taxes to the Donetsk People's Republic.

Russia has scathingly criticized the new Ukrainian authorities -- who came to power in February after a pro-Russian president fled -- for using the military against the rebellion. Ukraine is holding a presidential election on Sunday, which the government in Kiev hopes will unite the country behind a new leader.

Separatists exchanged fire again Tuesday with government forces on the outskirts of the eastern city of Slovyansk -- the epicenter of the rebellion against the government -- but this time anger at the fighting appeared to be growing.

Yekaterina Len, a 61-year-old resident whose house was hit by a mortar shell, burst into tears as she looked at the wreckage. She survived the shelling by spending the night with neighbors.

She and other residents sounded exasperated and angry with both warring sides. Some said many houses had been hit as rebels move around the area, shoot at government troops and draw retaliatory fire.

"They must stop with this banditry so that there can be peace!" said resident Lina Sidorenko. "How much longer can this go on? We had a united country and now look what's happened."

Vyacheslav Ponomaryov, the separatist leader in Slovyansk, later heard an earful as he met with about 200 residents. Many angrily shouted demands at him to end hostilities.

Wearing a pistol on his belt and flanked by a bodyguard toting a Kalashnikov rifle, Ponomaryov yelled back at the crowd, saying he will compensate those whose houses were damaged.

"Please, I implore you, do not panic!" he shouted. "If you do, you are playing into the hands of our enemies."

He also lashed out those in the crowd who blamed the insurgents for putting civilians at risk.

"Why are you shouting at me?" he yelled. "You only care about your own matters!"

Russia's Defense Ministry, meanwhile, said its units were dismantling their camps along the border with Ukraine and preparing to leave for their home bases.

A day after President Vladimir Putin issued a pullout order in an apparent bid to ease tensions with the West, the ministry said the army units in the Bryansk, Belgorod and Rostov regions bordering Ukraine were getting ready to leave.

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 a change.

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

The Russian Defense Ministry said it would take time for troops to dismantle their camps and load equipment on trucks for a march to railway stations. It didn't say how many troops were being pulled out or how long it would take.

Footage broadcast by Russian television showed what it said were troops on their way out, but their exact locations and routes remained unclear.

Putin's order to withdraw troops from areas near the border and his support for Ukraine's presidential vote, which he had previously sought to postpone, appeared to reflect a desire to de-escalate the worst crisis between Russia and the West since the Cold-War era.

The U.S. and the European Union have imposed travel bans and asset freezes on Putin's inner circle over Russia's annexation of Ukraine's Crimea Peninsula. They have threatened to target entire sectors of the Russian economy with sanctions if Russia tries to grab more land or attempts to derail Ukraine's presidential election.