Visiting Israel two days before Prime Minister Ariel Sharon and Palestinian President Mahmud Abbas meet in Egypt, Rice said Israel had to make some hard decisions and encouraged it to press its Gaza pullout plan and not to seize lands around Jerusalem.
She also said that Palestinians should wage "an effective fight against terrorism".
Criticised for too little involvement in Middle East peace efforts in his first term, US President George Bush sent Rice to the region to back up his pledge to press harder for an end to the conflict.
But with both sides about to embark on a new dialogue, Rice's mission seemed less of an arm-twisting exercise and more of an affirmation of change after Palestinian leader Yasir Arafat's death in November.
Rice is due to meet Abbas in the West Bank on Monday.
The peace credentials of Arafat's successor, Abbas, were further boosted on Sunday when his ruling Fatah movement re-issued a call for a mutual ceasefire with Israel.
Rice will not attend the summit
with Sharon (L) and Abbas
In a statement, the 124-member Fatah Revolutionary Council said its member militias would refrain from attacking Israeli civilians inside Israel and would be ready for a mutual ceasefire in lands Israel captured in the 1967 Middle East war.
In addition to the ceasefire call, the 25 members of Fatah's higher committee, which conducts the group's daily affairs, tendered their resignations in a bid to pressure the movement to bring forward an internal election planned for August.
Fatah, founded by the late Arafat, has not held elections since 1989.
Hope and responsibility
Rice praised a new Palestinian leadership that has "expressed its desire for a peaceful future with Israel" and Sharon's drive to dismantle all settlements in Gaza and four in the West Bank.
"This is a hopeful time, but this also is a time of great responsibility for all of us to make certain that we act on the words that we speak," she said, standing next to Sharon.
She said it now appeared possible "to get back on to the road map," a peace initiative backed by the UN, US, EU and Russia, which has been stalled by violence.
Rice said Washington was looking at ways it could help the sides monitor any ceasefires, coordinate security measures or establish mechanisms for the sides to defuse crises.
No foreign mediation
Aljazeera's Jerusalem correspondent, Walid al-Umari, said Rice's visit to Israel was received coldly as Israelis were against US mediation and preferred direct dialogue with the Palestinians.
"This is a hopeful time, but this also is a time of great responsibility for all of us to make certain that we act on the words that we speak"
US secretary of state
Rice will not attend the summit in the Red Sea resort of Sharm al-Shaikh, signalling she preferred to see Sharon and Abbas make progress as free of foreign mediation as possible.
"I hope we would all get into a mindset that says if the parties are able to continue to move on their own, that's the very best outcome," the newly appointed secretary of state - on an eight-day tour of Europe and the Middle East - said earlier in Ankara.
Al-Umari also said the Israelis were not satisfied with any US proposal which might prevent them from carrying out rapid reactions against Palestinian operations.
He was speaking in reference to a US initiative set up to revive the security plan between Israelis and Palestinians that was under CIA supervision.
But reports prior to Rice's visit said the White House had vowed not to offer the initiative at the present time.