"Is there popular will to hold early presidential elections? If there is, I don't have a problem with it," Assad told Russian state news agency RIA Novosti, according to an Arabic-language transcript provided by Damascus.
Assad's term is set to end in 2021, but a peace process backed by world powers envisages UN-monitored parliamentary and presidential elections within the next 18 months.
Assad's future -- including whether he would be allowed to run in those elections -- remains controversial. The opposition insists he must stand down.
Syria last held a presidential poll in June 2014, when Assad was re-elected for a seven-year term with 88.7 percent of the vote.
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At the time, polling took place only in government-controlled territory and in several dozen countries that have not cut diplomatic ties with Syria's government, including Lebanon.
Assad said all Syrian citizens would have the opportunity to vote in a future presidential vote.
"It would include every Syrian, whether he is inside Syria or outside Syria... Every Syrian citizen in every part of the world has the right to vote," he said in the interview.