Simultaneously, the Palestinian leader sent a letter to US President Barack Obama, in which he reiterated the Palestinian demand for a peace agreement based on an independent Palestinian state within the June 1967 borders.
Abbas stressed in his letter that the American administration must pressure Israel to solve all the permanent agreement issues, adding that the settlements were an obstacle to the peace process.
The Palestinian president added in an interview to Egyptian media that the negotiations with Israel must be held based on the Arab peace initiative.
'No middle-ground solutions'
Meanwhile, a top Palestinian negotiator said that the Palestinians would reject any deal between Israel and the United States that would allow even limited Jewish settlement construction in the West Bank.
"There are no middle-ground solutions for the settlement issue: either settlement activity stops or it doesn't stop," Saeb Erekat told Voice of Palestine radio. He added that Abbas had expressed that message his letter to Obama on Saturday.
Erekat was responding to reports that Israel and the United States were discussing a compromise that would allow some building in existing settlements under what Israel terms "natural growth" to accommodate expanding families.
A US official denied on Wednesday a report in an Israeli daily that the Obama administration agreed work could continue on 2,500 housing units whose construction had begun, despite its call for a total freeze to spur peace efforts.
The US State Department said Mitchell was expected in the region "soon" for talks with Israeli and Palestinian officials.
Barak has been seeking a deal with the United States that would include initial steps by Arab states to normalize relations with Israel in return for limiting settlement activity.
Reuters contributed to this report