The aim of Mitchell's latest trip to the region is to get Israel to agree to a compromise on settlement construction that would be acceptable to the Palestinians and enable a resumption of peace negotiations after they were suspended in late December amid the Israeli war on Gaza.
"I am here because President Obama ... has deeply and seriously committed to comprehensive peace in the Middle East, beginning with a two-state solution," Mitchell reiterated on Tuesday.
Nour Odeh, Al Jazeera's correspondent in Ramallah, said: "What Palestinians will probably celebrate ... is that they were able to survive the immense pressure applied by the American envoy and the American administration to push the Palestinian president into a trilateral meeting with his Israeli counterpart, Binyamin Netanyahu, and with the American president on the fringes of the UN general assembly later on this September."
Earlier in the day, Mitchell met Netanyahu, with whom he was due to hold more talks on Wednesday as part of his trip to the region.
One day before his talks with Mitchell, Netanyahu repeated that he had no intention of implementing a complete freeze, saying any halt would be temporary, would not extend to occupied east Jerusalem, and would exclude some 2,500 units already under construction.
Odeh said: "There is a lot of frustration about the lack of weight the Arab position has had in this equation.
"The Arab position, in support of the Palestinian president in refusing to meet [Netanyahu] before a settlement freeze ... hasn't really pushed the Obama administration to apply serious pressure ... on the Israeli government that previous American administrations have done.
"There is a question of political will … and how it [the US] sees this will better serve its own purposes domestically and internationally.
"It will be very difficult for Abbas to go back on his word without delivering something substantive to the public in exchange for meeting with Netanyahu."
The contiued construction of Jewish settlements on occupied Palestinian land, already home to half a million Israelis, is one of the major obstacles in reaching a peace deal with Palestinians.