Under the proximity talks, Mitchell will shuttle between the Israeli and Palestinian leaders to try to narrow their differences.
But the decision to back talks followed "indecision and dissent," Al Jazeera's Nour Odeh, reporting from Ramallah, said.
"There was disagreement during the discussions but once the decision was taken to move ahead it became the official Palestinian positions. But a variance in positions and perspectives from different political factions is not unusual in the Palestinian political system," she said.
The talks also faced opposition in the Gaza Strip, where Hamas, the Palestinian group which governs the Palestinian enclave, called on the PLO to reject the resumption of talks, dismissing them as "absurd".
"We warn the executive of PLO not to take any decision to resume talks with the enemy and to give cover to the Israeli occupation to commit more crimes against our people," Hamas said in a statement.
Our correspondent said: "Hamas, which has not participated in these inter-Palestinian discussions, has regretted the PLO executive committee decision and has said that this will only serve to provide the Israelis with cover while they continue to confiscate more land for the purposes of illegal settlements."
Khalil Shaheen, a political analyst in the West Bank, said the Palestinian people do not consider the PLO-Fatah meeting representative of all Palestinians.
"Take into consideration that Hamas is not a member of the PLO and we have some factions on the left that are against and reject direct or indirect negotiations," he told Al Jazeera.
"For the Palestinians, they are more concerned about the coming change in [the Palestinian] government more than they are concerned about negotiations that will not bring them any breakthrough towards establishing their own Palestinian state."
Negotiations between the Palestinians and Israel have been stalled since Israel's three-week assault on the Gaza Strip began in December 2008.
|Attempts to restart talks in March collapsed when Israel announced new housing projects
Attempts to restart the stalled process in March collapsed when Israel announced construction of a new housing project in occupied East Jerusalem,which Palestinians see as the future capital of any independent state.
The talks will not be the face-to-face meetings the administration of Barack Obama, the US president, had hoped to put in place, but will involve US officials meeting with one side at a time.
Mitchell has been shuttling between Israeli and Palestinian leaders in a bid to relaunch the dialogue.
He met Shimon Peres, the Israeli president, on Friday who said Israel is ready to negotiate with the Palestinians.
The Palestinians have said they want the indirect talks to focus on the final borders of their future state.
Binyamin Netanyahu, the Israeli prime minister, announced a 10-month settlement freeze in the West Bank in November.
Abbas' timetable for indirect talks will roughly coincide with the end of that freeze.
Israeli officials have said repeatedly that they will not approve another halt in construction, regardless of what happens during negotiations.