Syria is a country with talented people and a long and impressive history, he said, but it needs real peace to achieve its full potential.
His remarks closely mirrored those he made June 13 when he was last in Damascus.
'We seek peace between the Palestinians and Israelis, between Syria and Israel, between Lebanon and Israel and full normalisation between Israel and its Arab neighbours,' he told reporters then.
Mitchell, who met with Barak in Tel Aviv in the mid-afternoon, is only one of several top US officials visiting the region this week. Defence Secretary Robert Gates was expected in Israel and Jordan later Sunday. National Security Advisor James Jones and administration official Dennis Ross are also expected in the coming days.
Their visits come amid sharp differences between Israel and the Obama administration over the question of Israeli settlement construction in the occupied territories, with Washington demanding a total halt to Israeli building.
Israeli Prime Minister Benjamin Netanyahu attempted to minimize the rift, telling his ministers before the start of Sunday's cabinet meeting in Jerusalem that it was only 'natural' that Israel and the US would not be in full agreement on all points.