KIEV, Ukraine — Pro-Russian separatists in eastern Ukraine on Tuesday faced an unaccustomed wave of anger from residents who expressed frustration over the violence and instability in the region, particularly recent mortar attacks around the embattled city of Slovyansk that have damaged several homes and terrorized residents.

The separatist movement has been showing signs of strain since President Vladimir V. Putin of Russia said this month that he intended to pull back his troops from the Ukraine border, encouraged a national dialogue and tentatively backed Ukraine’s coming presidential election. Steelworkers easily wrested control of the port city of Mariupol last week under the direction of Ukraine’s richest man, Rinat Akhmetov, who owns the mills where they work, and Mr. Akhmetov has continued to pressure the separatists.

Thousands of Mr. Akhmetov’s employees took part on Tuesday in highly choreographed rallies throughout the region, collectively known as Donbass, to show support for Ukrainian unity and to denounce the continuing unrest. But the turnout fell far short of the hundreds of thousands that Mr. Akhmetov had hoped would attend.

In Slovyansk, a center of rebel activity, the separatist mayor, Vyachislav Ponomaryov, was accosted by some of the 200 residents in attendance at what resembled an impromptu, open-air town meeting. They demanded he put an end to the violence, which continued Tuesday with mortar shelling and sporadic gunfire on the outskirts of the city.