"There will be no negotiations without international legitimacy and a complete halt to settlements," he told the cheering crowds that had gathered at his Ramallah headquarters to welcome him back from the United Nations.
The massive turnout underscored the sudden surge of popularity Abbas is enjoying in the wake of his request that the UN admit a state of Palestine as a full member.
But his comments appeared to be a rejection of a proposal for new peace talks offered by the Quartet on Friday, shortly after Abbas submitted the UN membership bid on Friday.
The group, comprising the United States, United Nations, Europe and Russia, called for talks to begin within a month, and for a final deal to be reached before the end of 2012.
But they made no explicit reference to a halt of Israeli settlement construction, or clear parameters for the talks, both of which the Palestinians have said are key preconditions for their return to the negotiating table.
In Washington, Israeli Prime Minister Benjamin Netayahu told NBC television's "Meet the Press" programme that the Palestinians wanted a state "without giving Israel peace, or giving Israel peace and security."
Netanyahu said he had this advice for Abbas: "If you want to get to peace, put all your preconditions to the side."
In Ramallah, Abbas arrived directly at the Muqataa, his presidential compound, which was packed to capacity for a welcome party in his honour.
He told the crowds he had conveyed their dreams of statehood to the international community with his address to the UN General Assembly and formal submission of the membership bid.
"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.
"I have no doubt that the whole free world from one end to the other received what we told them about you and your dreams with all due respect," he added as the crowds chanted "The people want a Palestinian state."
"Brothers, there is no doubt that we are strong, strong in our rights, strong in our determination; our eyes, our minds and our culture are strong," he said.
"Lift your heads up high, you are Palestinian!"
The crowds applauded wildly, waving the Palestinian flag and the yellow banner of Abbas's Fatah party.
Thousands had begun gathering at the Muqataa several hours before Abbas arrived, responding to calls from local unions, the Fatah movement and the campaign that was organised to back the UN bid.
Buses laid on by different groups brought cheering Palestinians from cities including Hebron in the south and Jenin in the north, organisers said.
Ahead of Abbas's arrival, Mohammed Amudi said he had come to show his support for the unassuming Palestinian leader.
"I came to the Muqataa to declare my support for Abu Mazen's brave speech at the United Nations and his challenge to the United States," he said, using Abbas's popular nom de guerre.
Nearby, 71-year-old Abed Qader Mohammed sat holding a Palestinian flag.
"I came to show solidarity with Abu Mazen because I believe that his speech to the UN was not just his speech, but our speech," he said.
"Abu Mazen did his job at the UN and put our demands on their table and I'm here at the Muqataa today to say to him: thank you."
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@Ariely: You are the guys occupying their land and building more settlements. And then you are bring so sanctimonious!
Fool me once: shame on you! Fool me twice- shame on me How Palestinians negotiate? Lets assume is a cake! Step1: Before starting negotiations you have to give me a present Step2: The present is insignificant. Give me something more significant. Step3: OK. We are negotiating: Half of the cake is mine. Let's negotiate about the other half.
Step 4: Palestinian are telling to Arab world that the cake negotiation is a game played with infidels> Palestinians renew indiscriminate violence
Step 5: After been tired of the current violence stage they say : Lets have a brake and start negotiations. Sep 6: They demand to start the negations from what has been left of the cake from of the previous negations> The farce peace negotiation cycle restart from Step 1.