In an interview with Israel TV, Abbas also said negotiations with Israeli Prime Minister Benjamin Netanyahu remain his preferred choice, but that he will consider other options if talks break down over Israel's continued settlement expansion.
Negotiations were relaunched by the Obama administration last month, but quickly faltered over Israel's refusal to extend a curb on Jewish settlement construction. Abbas says there's no point negotiating as long as settlements take over more land claimed by the Palestinians.
The Palestinians want to establish a state in the West Bank, Gaza and east Jerusalem, captured by Israel in 1967. Israel has withdrawn from Gaza, but about half a million Israelis have settled in the other war-won areas.
Netanyahu wants the Palestinians to recognize Israel as a Jewish state, and said earlier this week he might extend a curb on settlement construction in exchange for such recognition. A 10-month-old moratorium on West Bank housing starts expired in late September, and Abbas has said he will not return to negotiations without an extension.
The Palestinians argue that it's not up to them to determine the nature of the state of Israel. Abbas noted that Israel and the Palestine Liberation Organization recognized each other in 1993, saying this should be sufficient. Abbas heads the PLO.
However, in an apparent attempt to reach out to Israeli public opinion, he said that once the Palestinians have established their state in the 1967 borders, "there is another important thing to end, the conflict, and we are ready for that, to end the historic demands."
He did not elaborate on specifically which demands he was relinquishing, but traditionally Palestinians have demanded the right of Palestinian refugees to return to their homelands in Israeli territory.
Asked about options if talks collapse, Abbas said the Palestinians might turn to the U.N. Security Council to seek recognition of their state. "All the options are open, but we don't want to use all of them right now. We are focusing on resuming direct talks," he said.
He said that for the time being, he has not considered resigning or dissolving the Palestinian Authority, his self-rule government which has limited control over about 40 percent of the West Bank.
Abbas defended his decision not to resume talks until Israel curbs settlements, noting that the international community is unanimous in its demand for a settlement freeze. "When (President Barack) Obama came to power, he is the one who announced that settlement activity must be stopped," Abbas said. "If American says it and Europe says it and the whole world says it, you want me not to say it?"
Since the start of negotiations, Abbas said he spent about 25 hours talking to Netanyahu directly, and that they spoke freely.
Abbas said that when he appealed to Netanyahu to halt settlement building, the Israeli leader told him his government would fall. Netanyahu heads a center-right coalition with several pro-settlement parties.
"I told him this is a historic opportunity for you that we sign a peace agreement," Abbas said of his conversations with Netanyahu. "I am afraid if we can't do it these days, the opportunity will be lost."
In other developments Sunday, Netanyahu said Israel has resumed indirect talks with the Hamas rulers of Gaza about swapping hundreds of Palestinian prisoners for a captive soldier held for more than four years. The German mediator who has been working to broker a deal to bring home the soldier for about a year has returned to the region, Netanyahu said. The soldier was captured in 2006.
In northern Gaza, meanwhile, an Israeli airstrike killed two militants.
The Israeli military said its air force targeted a squad of militants preparing to fire rockets at Israel.
The militants' affiliation was not immediately known, but they did not appear to be connected to Hamas or any other major group since there was no claim of responsibility.
The Israeli military said more than 165 rockets and mortars have been fired at Israel from Gaza so far this year.
Associated Press writer Dalia Nammari contributed to this report from Jerusalem.