Alexander Zakharchenko said the October 18 vote would be conducted "on the basis of Ukrainian law...In the parts where it does not contradict the constitution and law" of the self-proclaimed Donetsk People's Republic.
Eastern Ukrainian insurgents and Kiev don't agree on the implementation of a peace deal signed with the help of Germany and France in February that is designed to end the ex-Soviet country's bloody 15-month war.
The so-called Minsk II accord requires the two sides to hold immediate consultations about elections that could be conducted in rebel-run parts of the Donetsk and Lugansk regions before the end of the year.
The separatists have also previously threatened to bar any local official who backs Kiev's rule from running for any office.
Zakharchenko's vague comments about how exactly the planned vote would take place drew a cautious but largely negative response from the Western-backed president of Ukraine.