He said that "any future Palestinian government" would honour all past agreements that the Palestine Liberation Organisation and the Palestinian National authority had committed to.
These, he said, included letters between the Palestinians and Israel in which the PLO agreed to recognise Israel, renounce violence and commit to negotiations aimed at creating an independent Palestinian state alongside the state of Israel.
Abbas has been negotiating a unity government between his Fatah movement and Hamas, which took power in March after a sweeping election victory.
He said that if a unity government led to a resumption of peace negotiations with Israel, they would be under the jurisdiction of the PLO, which he heads. In addition, any results would be submitted either to a national referendum or the Palestinian National Council.
He said: "Any future government will commit to imposing security and order, to ending the phenomena of multiple militias, indiscipline and chaos, and to the rule of law."
He added that such commitments "should suffice to lift the unjust siege imposed on our people, which has inflicted extensive damage on our society, its livelihood and means of its growth and development".
He also recalled the plea issued from the General Assembly podium 32 years ago by Yasser Arafat, the then PLO chairman, who pulled out a gun and an olive branch and said: "Do not let the olive branch fall from my hand."
Abbas said: "And here I am repeating the same call: Do not let the olive branch fall from my hand, do not let the olive branch fall from my hand."