"There is no transition period. There exist official institutions that are functioning," Faisal Moqdad said on a visit to Tehran, Syria's state news agency SANA reported.
"We are talking about a national dialogue, an enlarged government and a constitutional process, not a transitional period," he added.
Moqdad's comments come after a round of international talks in Vienna last week to discuss a potential end to Syria's four-year conflict.
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Neither Syria's regime nor opposition were represented, but countries backing either side were present.
A transitional government has long been discussed as part of a peace process to end Syria's conflict, from as early as 2012, when world powers met in Geneva to discuss the war.
The fate of Assad has been a persistent sticking point in discussions on ending the conflict, however, with the regime and its backers insisting he will not be forced from power.
"President Bashar al-Assad is the legitimate president elected by the Syrian people, and the world must respect that will," Moqdad said on Tuesday.
Syria's opposition and its backers insist Assad can have no role in the country's future.