Ehud Olmert, the Israeli prime minister, had floated the idea last week.
Such a declaration, as envisioned by Israel, would outline the contours of a future Palestinian state, without immediately tackling the most explosive issues, such as final borders and the fate of Palestinian refugees.
Abbas suggested he is ready to consider the idea.
Israeli-Palestinian talks would "focus on implementing what was mentioned in the road map," he said, referring to the international peace plan that envisions a Palestinian state alongside Israel.
"Then we could end in a declaration of principles," Abbas said during a joint news conference with Rice.
"The important thing here is that we reach results, and that we know the ceiling [final stage], but the stages of implementation can be agreed upon," Abbas said.
Abbas also told Rice that he was working to improve security in the Palestinian territories.
"We are continuing our efforts to improve the security situation," he said.
He told the news conference: "We want to achieve a Palestinian state and security."
Rice said an international peace conference being promoted by the administration of George Bush, the US president, for this autumn "is not to get people together for a photo op" but rather "so that we can really advance Palestinian statehood".
Earlier in her four-day tour, Rice met Salam Fayyad, the Palestinian prime minister, in Ramallah, the seat of Abbas' Western-backed government.
She also met the Palestinian cabinet, a gesture of support for the team that replaced the Hamas government after the group seized Gaza by force.
|"Ultimately, the Palestinian people will have to choose what kind of world they will live in, what kind of state they will have" |
Condoleezza Rice, US secretary
Rice's meeting with Abbas is the first since Hamas took control of Gaza.
When Hamas took control of Gaza from Abbas's Fatah forces in mid-June, the president of the Palestinian Authority fired the group from the government and installed a new cabinet in the West Bank.
"Ultimately, the Palestinian people will have to choose what kind of world they will live in, what kind of state they will have," Rice said, at the end of a four-day Middle East trip.
The tour is partly aimed at laying the groundwork for an international peace conference that the United States will host later in the year.
Abbas received a boost this week after Moscow downgraded its contacts with Hamas, while maintaining some ties with the group to foster dialogue.
The decision came after Abbas met Vladimir Putin, the Russian president, in Moscow which, according to a Russian official, has taken a dim view of Hamas's use of force to take control of Gaza.
A US official cited "very interesting" reports about the Abbas-Putin talks in an indication that Rice would be anxious to get details of the Moscow encounter from the Palestinian leader.
Rice travelled with Robert Gates, the US defence secretary.
They travelled together to Egypt and Saudi Arabia before Gates went on to Kuwait while Rice headed to Israel and the Palestinian territories.