But organizers of Sunday's vote have said that only later will a decision be made on whether they would use their nominal sovereignty to seek full independence, absorption by Russia or to stay part of Ukraine but with expanded power for the regions.
Ukrainian President Oleksandr Turchynov, in comments posted on the presidential website Saturday, said supporters of independence for the east "don't understand that this would be a complete destruction of the economy, social programs and general life for the majority of the population."
"This is a step into the abyss for the regions," he said.
The elections chief of the insurgents in Donetsk, Roman Lyagin, was quoted by news agencies as saying voting in Mariupol and one other district had begun early because of rising tensions there. He did not elaborate.
At least seven people died Friday in clashes in Mariupol. The city remained on edge Saturday, with barricades of tires blocking some streets in the city center.
Turchynov and Ukraine's interim government came to power in February following the ouster of Russia-friendly president Viktor Yanukovych after months of protests in Kiev. Moscow and many in Ukraine's east denounce the government as a nationalist junta and allege that it intends to trample on the rights of eastern Ukraine's Russian-speakers.
More than 30 people have been reported killed as Ukrainian forces mount offensives to retake some eastern cities now under control of the insurgents.
In the remarks issued Saturday, Turchynov said the government was willing to negotiate with representatives of the east, but not with anyone he called "terrorists whose task is the destruction of the country, a task put forth by their masters."
Kiev claims Russia is fomenting or directing the unrest in the east, with the goal of destabilizing Ukraine or finding a pretext for invasion.