"The current US administration wants to find a solution to the crisis in Syria. There is a tacit agreement between the US and Russia to reach this solution," Bouthaina Shaaban said in an interview with state television late Wednesday.
"The US recognises now that Russia has profound knowledge of this region and a better assessment of the situation," she said.
"The current international climate is heading towards detente and towards a solution for the crisis in Syria."
Shaaban said there was a "change in the West's positions" over Syria's war, which has killed more than 240,000 people and displaced millions since 2011.
Russia, a decades-long backer of Syria's regime, has said it would not accept Assad's departure as a prerequisite for launching any peace process in the war-torn country.
While the United States has called for Assad's ouster for more than four years, Secretary of State John Kerry said last week that "it doesn't have to be on day one or month one or whatever."
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On Wednesday, French President Francois Hollande called for a new Syria peace conference "so that all the countries who want to see peace restored in Syria can contribute."
While Hollande maintained that there could be "no transition without (Assad's) departure," German Chancellor Angela Merkel said Thursday that the Syrian leader should be involved in the talks.
"We have to speak with many actors, this includes Assad, but others as well," Merkel told a press conference after an EU summit on the migration crisis sparked by the Syrian war.
The diplomatic flurry came amid concerns about increased Russian military support to Assad, including Moscow's announcement Thursday that it would hold naval drills in the eastern Mediterranean region in September and October.
On Wednesday, the Syrian military deployed Russian-supplied drones for the first time, a security source in Damascus said.
The army has received new weaponry from Russia for its fight against jihadists, including at least five fighter jets, a senior Syrian military official told AFP.