He said his efforts were now focused on preparing 'the context' for meaningful negotiations soon, based on 'mutual respect and mutual interests'.
The tour of the region was part of a US diplomatic blitz to restart negotiations for a 'comprehensive' Middle East peace, coinciding with a visit by Defence Secretary Robert Gates to Israel Monday.
Gates is now in Jordan, where he will continue to hold meetings Tuesday.
Meanwhile, James Jones, Obama's national security advisor, and administration official Dennis Ross were also expected in the coming days.
After Mitchell's hour-long meeting with al-Assad Sunday, his second since June, he told reporters that he had discussed the prospects for a comprehensive peace in the region and improved relations between Syria and the US.
'That peace means between Palestinians and Israelis, between Syria and Israel, and between Lebanon and Israel. And of course, ultimately, the full normalisation of relations between Israel and all of the countries in the region,' Mitchell said.
'This is what the Arab Peace Initiative calls for, and it is the ultimate aim of the effort we are undertaking,' he added.
In 2002, members of the Arab League offered to establish full diplomatic relations with Israel in exchange for a full Israeli withdrawal from the territories it occupied in the 1967 war and 'a just' solution to the question of Palestinian refugees. Syria supports the initiative.
Mitchell reiterated the sentiments in his later meeting with Barak in Tel Aviv, saying normalised relations across the region are part of Obama's personal vision and goal. But achieving that vision requires all parties to take the necessary steps, he added.
The US envoy's visit to Tel Aviv comes 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.
On Tuesday Mitchell is to hold talks with Israeli Prime Minister Benjamin Netanyahu.