Mitchell is the most senior US diplomat to visit Syria since Barack Obama was elected as US president.
The US envoy arrived late on Friday from the Lebanese capital, Beirut, where he pledged that Lebanon, which has conflictive ties with Syria, would "play a key role ... to build lasting comprehensive peace and stability in the Mideast".
"We all share an obligation to create the conditions for the prompt resumption and early conclusion of negotiations"
George Mitchell, US envoy to the Middle East
Syria had expressed its readiness earlier this week to resume contact with Israel through Turkish intermediaries, on reigniting peace talks largely based on the fate of the disputed territory of the Golan Heights.
Last year, Turkey brokered four rounds of indirect talks, but Syria suspended them in December when Israel launched its war on Gaza.
The new Israeli government of Binyamin Netanyahu, the prime minister, has ruled out meeting Syria's demand for the return of the Golan plateau, which Israel seized in its six-day war in 1967.
The Israeli cabinet's decision drew an angry reaction from al-Assad at the time, who described Israel as "the major obstacle to peace".
Mitchell, who has already visited Israel, the West Bank, Egypt and Jordan, said earlier this week that he wants Middle East peace talks to resume soon.
"We all share an obligation to create the conditions for the prompt resumption and early conclusion of negotiations," he said in Jerusalem on Wednesday.
The US government has been pursuing diplomatic engagement with Syria.
In Cairo on Thursday, Mitchell urged Arab states to take "meaningful steps and important actions" to make peace with Israel.
The US imposed economic sanctions on Syria in 2004 over charges that it was a sponsor of terrorism. They have been extended several times since.
Relations deteriorated after the US-led invasion of Iraq in 2003, and the assassination of Rafiq al-Hariri, a former Lebanese prime minister, in 2005.
Under international pressure, Syria withdrew soldiers from Lebanon following the killing, and has denied any involvement.
The murder prompted the US to withdraw its ambassador to Syria, and a diplomat has yet to be reinstated.