Iran has yet to reply, the officials said.
The next diplomatic round starts Thursday in Vienna, with Secretary of State John Kerry, Russian Foreign Minister Sergey Lavrov and several top European and Arab diplomats attending.
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The United States is taking a gamble. Iran has backed Assad's government throughout the conflict, fighting alongside the Syrian military, and is seen by Western-backed rebels and US partners in the region as a major source of the bloodshed.
The Syrian opposition may balk at Iran's inclusion in any discussions on what a post-Assad Syria should look like.
On the other hand, all previous international mediation efforts have done nothing to stop the fighting, and Kerry is trying to unite all sides with influence in the Arab country around a common vision of a peaceful, secular and pluralistic Syria governed with the consent of its people.
The American officials weren't authorized to speak publicly on the matter and demanded anonymity. They said Russia extended the invitation.
Iran's supreme leader, Ayatollah Ali Khamenei, ruled out new negotiations with the United States after they and five other nations clinched a long-term nuclear agreement in July.
The US, Russia, Saudi Arabia and Turkey met last week in Vienna, putting forward new ideas to revive diplomatic hopes.
However, they remained deeply divided over Assad's future.
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