Foreign Minister Adel al-Jubeir made the comments after meeting his Egyptian counterpart in Cairo, and a day after Saudi Arabia and the United States called for more international efforts to restore stability in Syria without Assad.
"There are ongoing international consultations on implementing the Geneva 1 proposal," Jubeir told a news conference, referring to a 2012 initiative for a transitional Syrian government.
"I think there has been some progress so far and positions are coming closer...But I can't say we've reached an agreement and there needs to be more consultations," he said.
"We are committed to implementing the principles of Geneva to establish a transitional authority that installs a constitution and directs the government and military ahead of elections," he said.
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"And Bashar al-Assad will have no role in Syria's future. That is the position of the kingdom and that is the position of most countries in the world," he said.
US Secretary of State John Kerry and King Salman of Saudi Arabia yesterday called for greater international efforts to restore stability to Syria without Assad at its helm.
But the Vienna talks failed to make any breakthrough and Kerry said at the time he hoped to reconvene another "broader" meeting on Syria as early as October 30.
Russia and the West have been at loggerheads over Assad's fate, a major sticking point in efforts to solve a crisis that has killed more than 250,000 people since 2011 and sparked an exodus of around four million refugees.
Seeking to shake off months of Western isolation over the Ukraine conflict, Putin last month launched air strikes in Syria and has since held talks with the war's key regional players, including some of Assad's worst enemies, such as Saudi Arabia and Turkey.