An AFP reporter saw Abbas descend from his motorcade on Sunday and enter the presidential building known as the Muqataa.
He walked solemnly into the compound accompanied by a presidential honour guard, and immediately to the grave of his predecessor, Yasser Arafat, where he laid a wreath.
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As the crowd chanted "with our souls and our blood we will sacrifice for you Palestine", Abbas spoke of his request to the UN on Friday for a state of Palestine to be admitted as a full member of the world body.
"We went to the United Nations carrying your hopes, your dreams, your ambitions your suffering, your vision and your need for an independent Palestinian state," he said.
ISRAEL SEEKS TALKS
Israeli Prime Minister Benjamin Netanyahu says Palestinian leader Mahmoud Abbas should agree to talks without preconditions in order to achieve a long-delayed peace deal.
"The Palestinians want a state, but they have to give peace in return. What they're trying to do in the United Nations is to get a state, without giving Israel peace, or giving Israel peace and security," Netanyahu told NBC television's Meet the Press program on Sunday.
"That's wrong. That should not succeed, that should fail," the Israeli leader said.
He said that he broached the subject of talks without conditions with Abbas on the sidelines of last week's UN General Assembly.
"I said in the UN, I said to President Abbas, 'Look we're in the same city. We're in the same building, for God's sake, in the UN. Let's just sit down and begin to talk peace."
Netanyahu said he had this advice for Abbas: "If you want to get to peace, put all your preconditions to the side."
He made his remarks after Abbas was greeted back home in Ramallah by thousands who gathered to welcome him back from his bid to secure full UN membership for a state of Palestine.
Abbas told cheering crowds that Palestinians would not hold peace talks without a "complete halt" to Israeli settlement building.
"There will be no negotiations without international legitimacy and a complete halt to settlements," he said in comments which appeared to be a rejection of a proposal for new talks from the international peacemaking Quartet, which on Friday proposed renewed negotiations but did not explicitly seek a settlement freeze.
