He also called for an international probe to determine who killed Yasser Arafat after scientists said it was likely he had been poisoned.
Abbas was speaking in an exclusive interview at his Muqataa headquarters in Ramallah a day ahead of a key visit by French President Francois Hollande for talks expected to focus on the peace process.
In the interview, he reaffirmed his commitment to push ahead with the US-backed talks, despite a major upset over Israeli settlement building.
"We are committed and we will go to the full nine months, and then we will take the appropriate decision," he said, without elaborating.
After months of intensive shuttle diplomacy by US Secretary of State John Kerry, Israel and the Palestinians finally agreed to begin direct talks in late July with the ambitious aim of reaching an agreement within nine months.
As part of the deal which brought the two sides back to the table, the Palestinians agreed to suspend all efforts to seek international recognition for the duration of the talks.
But over the past three months, Israel has announced plans to build thousands of new settler homes on land the Palestinians want for their future state, sparking a chorus of furious denunciations from Ramallah.
On Tuesday, Israel said it would build 20,000 more settler homes in its biggest ever announcement, although the move was swiftly overturned by Israeli Prime Minister Benjamin Netanyahu.
A day later, the Palestinian negotiating team led by Saeb Erakat resigned in protest although their resignation was never formally accepted by Abbas.
"The Palestinian people know that the way to peace is through negotiation. But they also know we are insisting on Palestinian constants," he said -- namely an agreement based on the lines which existed before the 1967 Six-Day War, east Jerusalem as the capital of the future state, and resolution of the issue of the Palestinian refugees who fled or were forced out of their homes when Israel was established in 1948.
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