Crowley said that Mitchell will also meet Israeli and Palestinian officials during his visit to the region, as well as hold talks in Egypt and Bahrain.
Al Jazeera's Zeina Awad, reporting from Damascus, said: "On his first trip, [Mitchell]said that the Obama administration considers Syria to be an integral part of any future comprehensive deal.
"But Syrians are saying that they'd like to move beyond rhetoric and into some concrete action and measures on the ground.
"The Syrians have been extremely consistent with their position and they believe complete withdrawal from the Golan Heights is a prerequisite for talks on details such as how to share water from the Golan and the kind of role Syria could play when it comes to exerting pressure on groups that Israel considers to be an enemy.
Walid al-Moallem, the Syrian foreign minister , said on Friday that he was looking forward to Mitchell's visit as it would help rebuild diplomatic ties between Washington and Damascus.
He also said that Syria would lobby Mitchell on the issue of the Golan Heights, a strategic plateau seized by Israel in 1967.
Barack Obama, the US president, has tried to re-engage with Syria since he took power in January, a significant change in direction after George Bush, his predecessor, cut all diplomatic ties with Damascus in 2005.
In a recent interview, Obama said: "There are aspects of Syrian behaviour that trouble us and we think that there is a way that Syria can be much more constructive on a whole host of these issues.
"But as you know, I'm a believer in engagement and my hope is that we can continue to see progress on that front," he said.
Syria's support for Hamas, the de facto government in the Gaza Strip, and its relations with Iran, mean that Damascus could be key in US efforts to forge a new peace process in the region.
Al-Moualem said on Friday that it it could play a role in helping to find a solution to the ongoing dispute between Western nation and Iran over its nuclear programme.
"We support [a] political solution for issues standing between Iran and the West," he said after talks with David Miliband, the British foreign minister.
"For that, we believe we can play a role but we cannot take decisions on behalf of Iran. They have to take their decisionsaccording to their interest."
Mitchell's visit to Syria and Israel coincides with high-level diplomatic visits to the Middle East the same week by Robert Gates, the US defence secretary, and James Jones, Obama's national security advisor.