Khaled Khoja, leader of the Syrian National Coalition, made the appeal at a press conference held from the group's base in Turkey.
The government has been pounding the eastern suburbs of Damascus known as Ghouta for days as part of a military campaign against rebel-held districts east and south of the capital Damascus. Douma, a sprawling town east of Damascus, has taken the brunt of the airstrikes.
He said Assad's "barbaric assault" on Douma constitutes a war crime and urged the UN to force the Syrian leader to stop indiscriminate bombardment of rebel-held territory.
Government batteries have rained shells and rockets on Douma and other rebel-held districts outside the city in attacks that activists say have been some of the worst they've seen, including dozens of barrel-sized bombs that are dumped from helicopters.
Meanwhile, rapid advances by government forces backed by Lebanese Hezbollah fighters south of Damascus slowed Thursday because of a snowstorm hitting the region.
Ahmad al-Masalmeh, an opposition activist in the southern city of Daraa, said snow fell in some areas south of Damascus, making it difficult for vehicles to move. He also said there was no government air force activity.
Syrian troops and Hezbollah fighters on Wednesday seized strategic hills and villages from rebels and a local al-Qaida affiliate near the Israeli-occupied Golan Heights in a surprise counteroffensive that alarmed Israeli officials.
