In an indication of the uncertainty surrounding the elections, voting started early Saturday at one school in Donetsk for reasons that were unclear. And after armed men threatened to kill a principal in the Luhansk region who did not want voting at her school, the central government said education officials should not take risks to oppose the polling.

The two provinces that will vote are predominantly Russian speaking, but that does not guarantee a majority would want to secede from Ukraine. A poll by the Pew Research Center released this month indicated that 70 percent of respondents in eastern Ukraine favored keeping the country united, 18 percent favored the right to secede and the remainder were undecided.

Those conducting the plebiscite here in Donetsk said they were leaving plenty of flexibility for future changes of course.

“We win the right for self-determination,” Mr. Lyagin said. “The next step will be another referendum when we ask, ‘Do we want to join Russia? Or, do we want to join Ukraine? Or do we want to become an independent state?’ There are many possibilities.”

At the news conference, Mr. Lyagin again underscored the narrative of the pro-Russian groups here that their movement is grass-roots and that, while embracing the Russian flag as a symbol, it is not beholden to Moscow.

The opinion of President Vladimir V. Putin of Russia, who on Wednesday asked the separatists in eastern Ukraine to delay their referendums, was less important, he said, than the opinions of residents here. “We don’t owe anybody anything,” Mr. Lyagin said.

It remains unclear what Mr. Putin’s motives were for suggesting a delay, but the central Ukrainian government is convinced the leaders of the self-styled republics are fronts for a Russian intelligence operation to destabilize Ukraine. After weeks of unrest in the east, pro-Russian groups occupy administrative buildings in about a dozen towns, control some highways, and have full control over one midsize city, Slovyansk.