"It is the right time to talk about this issue seriously," Abbas told reporters after he met Egyptian President Hosni Mubarak onTuesday.
Recent weeks have seen a growing momentum toward reviving Israeli-Palestinian peace talks, with Israeli Prime Minister Ehud Olmert meeting Abbas on Saturday and the Iraq Study Group, a bipartisan Washington commission, reporting to U.S. President George W. Bush that progress on the Israeli-Palestinian dispute would contribute to reducing the conflict in Iraq.
Abbas did not spell out why he was proposing that the negotiations with Israel be "backdoor" - meaning conducted out of the media spotlight. But as one of the architects of the Oslo peace accord between Israel and the Palestinians in 1993, he is known to champion quiet, informal diplomacy.
"We have the idea of a backdoor channel between us and the Israelis, with the participation of one or all members of the Quartet to discuss all the issues of the final status," Abbas said, referring to the four Western powers - the United States, Russia, European Union and the United Nations - that oversee the peace process.
Abbas said he had proposed backdoor negotiations to Prime Minister Olmert at their weekend meeting, and that the Israeli leader had no immediate objection and promised to consider it.
Abbas said he planned to discuss the idea with U.S. Secretary of State Condoleezza Rice when she comes to the Middle East next month.
"This is not secret negotiations, therefore, they would help more than they would harms," Abbas said.
Abbas made clear he wanted the talks to focus on the issues that have been the hardest to resolve in previous negotiations - the future of Palestinian refugees, the sovereignty of Jerusalem - which both Israelis and Palestinians claim as their capital, and the borders of the future Palestinian state.
It is not clear if Olmert would agree to tackle the thorniest issues rather than proceed by the more cautious route of step-by-step negotiations and interim agreements.
It is equally unclear what would be the reaction of Hamas, the party that dominates the Palestinian cabinet, to what might emerge from backdoor talks with Israel.
Hamas, which refuses to recognize Israel, is believed to favor a limited truce in exchange for its complete withdrawal from the West Bank and east Jerusalem.