Work at some polling stations in the largest separatist- controlled city of Donetsk was disrupted by a sudden intensification of hostilities.
Artillery and small weapons fire could be heard in northern districts of the city near the airport, which has been the focus of heavy fighting for weeks.
Separatist authorities argue that Sunday's votes in the Donetsk Peoples Republic and Luhansk Peoples Republic will lend legitimacy to their aspirations for self-determination.
"We have put too much at stake on the altar of the victory and through this election we are legitimizing our government and thereby separating from Ukraine even further," said rebel election chief Roman Lyagin.
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The White House has denounced the planned elections as being contrary to Ukraine's constitution.
In a statement, National Security Council spokeswoman Bernadette Meehan said Friday that the U.S. Is warning Russia not to use the results of the voting as a pretext to make military moves into Ukraine.
The EU and the United Nations have also criticized the vote, but the Russian Foreign Ministry has argued that the Minsk agreement foresaw local elections in the rebel-held territories between Oct. 19 and Nov. 3.
The vote has appeared under-resourced, campaigning has been negligible, and there are fears that unrest may break out on the day.
It is unclear how many people will be able to vote as rebel officials say they have no access to central Ukrainian electoral rolls. Polling station workers yesterday made final preparations by sticking rebel government labels over voting urns bearing the Ukrainian national emblem.
No established international monitoring group is overseeing the vote, although a motley group of European far-right and communist political activists has traveled to the region, offering to act as observers.