SLOVYANSK, Ukraine (AP) -- Pro-Russia separatists fighting government forces in eastern Ukraine faced local anger Tuesday and a new challenge from the country's richest man who demanded they end their rebellion.
Russia, meanwhile, said some troops were dismantling their camps along the border with Ukraine.
A day after President Vladimir Putin issued a pullout order in an apparent bid to ease tensions with the West, Russia's Defense Ministry said its forces in the Bryansk, Belgorod and Rostov regions bordering Ukraine were preparing to return to their home bases. NATO, which estimates that Russia has 40,000 troops along the border with Ukraine, said it's 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."
In eastern Ukraine, separatists exchanged fire again Tuesday with government forces on the outskirts of Slovyansk, a city that has been the epicenter of the rebellion against the government in Kiev. But this time local 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 the warring sides. Some said many houses has been hit when rebels moved around the area, shooting at government troops and drawing retaliatory fire.
"They must stop with this banditry so that there can be peace!" said Slovyansk 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 met with about 200 residents, many of whom angrily shouted demands at him to end hostilities. Wearing a pistol on his belt and flanked by a bodyguard toting a Kalashnikov assault rifle, Ponomaryov yelled back at the crowd, saying he will compensate those whose houses were damaged.
In another development, Ukraine's richest man, metals tycoon Rinat Akhmetov, rode the wave of public dismay with the hostilities to toughen his stance against the rebellion, saying it has devastated the nation's eastern industrial heartland.
In a video statement, Akhmetov issued a strong call 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" Tuesday at their companies by blowing sirens "in support of peace and against bloodshed" and keep up those protests in the coming days.
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 counter-terrorist operation."
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 and get insurgents to vacate the government buildings they had seized.
In his statement, Akhmetov vowed to challenge the insurgents who declared independence last week in the eastern regions of Donetsk and Luhansk.
"No one will frighten us, including those calling themselves a Donetsk People's Republic," he said.
One of the leaders of rebels in Donetsk, Denis Pushilin, retaliated 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 the toppling of a pro-Russian president, 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.
However, 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 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.
The U.S. and the European Union have imposed travel bans and asset freezes on members of Putin's inner circle over Russia's annexation of the 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.
Isachenkov reported in Moscow and John-Thor Dahlburg in Brussels contributed to this report.