Rice made the statements at a news conference at the end of a brief visit to the Middle East, after shuttling between the two sides for three days.
Rice also said her envoy will try to set benchmarks for implementing a cease-fire, including the halting of rocket fire from Gaza, and for improving the flow of Palestinian travelers and goods through Israeli crossings.
The secretary said doors had been opened during her visit and that she was laying the ground work for future peace talks. She said she believed it was still possible for a peace deal to be reached during U.S. President George W. Bush's term.
She said Olmert and Abbas showed flexibility. Rice said she would occasionally participate in the meetings between the two.
"The parties will also begin to discuss the development of a political horizon consistent with the establishment of a Palestinian state in accordance with the 'road map'," she said, adding that "new thinking" was needed to move the stalled peace process forward.
"We are not yet at final status negotiations. These are initial discussions to build confidence between parties," Rice said.
The chief Palestinian negotiator, Saeb Erekat, said Rice had "managed to keep the door open between us and Israel." While Israel had tried to limit discussions to humanitarian and security issues, he said, Rice ensured that talks would include a "political horizon," if not a final status deal.
Rice said her task had been complicated by the formation of a new Palestinian government, a coalition between Hamas and Fatah. Rice said a path to cooperation with the new government exists, but that it must first renounce terrorism.
Rice also called on Arab states to take an active role in Middle East peacemaking.
Rice also met briefly on Tuesday with the families of abducted Israel Defense Forces soldiers Gilad Shalit, Ehud Goldwasser and Eldad Regev.
During the 20-minutes meet, the families sought to have Rice join the efforts to release the abductees. The secretary of state said she is happy to help, but stressed that she cannot deliberate directly with Hamas and Hezbollah, saying she would seek the assistance of European intercessors in that matter.
This has been Rice's first meeting with the families of the abductees.
American officials had hoped that the secretary would announce a new diplomatic drive for talks toward Palestinian statehood.
But the hopes were dampened late on Monday, when she met with Olmert for a second time, with the prime minister expressing his strong opposition to any mention of the "core issues" in the final status agreement with the Palestinians - namely Jerusalem, the Palestinian refugees and the 1967 lines.
Following deliberations between the two, Rice decided she would not make any dramatic statements during the Tuesday news conference in Jerusalem, rather that she would summarize her diplomatic efforts in the region in recent days.
Echoing the lack of any substantive progress, Erekat told Haaretz Monday that there had been positive efforts on the part of the U.S., but there was no American plan before to resume negotiations.
The discussions between the two leaders will initially revolve around confidence-building measures, and will leave an opening for discussions on other issues in the future.
For her part, Rice will continue her periodic visits to the region, in which she will hold parallel talks with Israel and the Palestinians on all issues pertaining to the "political horizon."
Rice postponed the press conference, originally planned for Monday night, because of differences of opinion with Olmert over the content of her statement.
Rice made it clear to Olmert that she is trying to substantiate the concept of a "political horizon."
It appears that the compromise between their differing stances will be that the "core issues" will be mentioned in passing.
Olmert also asked that any formula for the resumption of negotiations be based on the road map and the stages it proposes (combating terrorism, dismantling outposts, a Palestinian state along interim borders and a final settlement).
Olmert also agreed to begin deliberations on less sensitive issues, such as the security arrangements of a future Palestinian state, and the conditions for implementing the agreement on the basis of the road map.
Olmert also opposed the proposal Rice made, that American mediation replace direct negotiations between Israel and the Palestinians.
Maintaining constant and fluid contact with Olmert is for the Palestinians, at this juncture, considered a priority.
Erekat said Monday that "one of the most important elements from the point of view of the PA is to maintain the channel of communication open between Abu Mazen [Abbas] and Olmert. There is no substitute for this."