US Secretary of State John Kerry made the demand during a phone call to Russian Foreign Minister Sergei Lavrov on Tuesday, the US State Department said in a statement.
"Secretary Kerry made clear that Russia's continued support for President Assad risks exacerbating and extending the conflict, and undermining our shared goal of fighting extremism," the State Department stated.
Kerry "reaffirmed the US commitment to fight ISIL with a coalition of more than 60 countries, of which Assad could never be a credible member, and emphasized the US would welcome a constructive Russian role in counter-ISIL efforts," it added, using an acronym by which the Daesh Takfiri group is known.
In his phone call, Kerry acknowledged that there is no military solution to the years-long Syrian crisis and called for a political solution to establish peace in the Arab country.
"The secretary stressed that there is no military solution to the overall conflict in Syria, which can only be resolved by a political transition away from Assad," the State Department said.
Syria has been gripped by deadly violence since March 2011. More than 230,000 people have reportedly been killed and millions displaced due to the violence mainly fueled by the foreign-sponsored militants.
The United States and its regional allies -- especially Qatar, Saudi Arabia and Turkey -- have been supporting the militants operating inside Syria since the beginning of the crisis.
The Obama administration has already outlined a $500 million program to train and arm 5,000 “moderate” militants in Syria to fight against ISIL and the Assad government, but according to the Pentagon, the number would be something between 12,000 and 15,000.
According to a report published by the New York Times on Monday, Russia is using the airspace over Iran and Iraq to fly military equipment and personnel to a new air field in Syria.
At least seven giant Russian Antonov An-124 military transport aircrafts have taken off from a base in Russia during the past week to transport equipment to Syria, using Iranian and Iraqi air corridors, the Times reported, citing US officials.
American officials told the newspaper on Sunday that the destination of the Russian aircraft was an airfield in Syria’s western province of Latakia.
About 200 Russian marines and six Russian howitzers now guard the air base in Latakia, according to American intelligence.
On Saturday, Kerry called Lavrov and warned that Washington is deeply concerned of reports of "an imminent enhanced Russian military buildup;" Press TV reported.