Arab states including Syria - a bitter opponent of Israel - will be asked to a Middle East peace meeting in November, the US secretary of state has said.
Ms Rice says the US wants Syria and Saudi Arabia involved in talks
Condoleezza Rice described the Arab nations as "natural invitees" but said they would have to renounce violence.
She was speaking after the four backers of the peace process - the US, EU, Russia and the UN - met in New York and gave support to the proposed summit.
The quartet issued a roadmap in 2003 for an Israeli-Palestinian peace deal.
But the roadmap has been sidelined and no apparent progress has been made towards achieving the declared aim of the process, a two-state solution.
After Sunday's meeting, the quartet issued a statement expressing support for the proposed conference - which has been heavily promoted by the US.
Ms Rice said it "would be natural" for Syria, Saudi Arabia and 10 other Arab League members to participate, but warned that attending the summit brought "certain responsibilities".
"We hope that those who come are really committed to helping the Israelis and the Palestinians find a way through - and that means renouncing violence, it means working for a peaceful solution."
Syria remains technically at war with Israel - Egypt and Jordan are the only Arab states to have signed a peace treaty with Israel.
BBC diplomatic correspondent Jonathan Marcus says the phrase "international meeting" is notable, perhaps indicating something short of a full-scale peace conference.
With the Palestinians divided and with Israel designating the Gaza Strip as hostile territory, the climate is not encouraging, he says.
The quartet also called for humanitarian assistance to Gaza to continue without obstruction - a warning to Israel, which has threatened to cut off vital energy supplies.
The quartet noted its grave concern about the continued rocket fire into Israel from the Gaza Strip, as well as what it termed recent efforts by the Hamas leadership there to stifle freedom of speech in the press.
The stakes over the coming weeks are high, our diplomatic correspondent says.
The quartet's envoy, former UK Prime Minister Tony Blair, said he believed the peace process now had momentum.
He said there was an "ambitious but achievable" plan to create a sense of how a Palestinian state would look by the end of the year.
UN Secretary General Ban Ki-moon chaired Sunday's talks with his quartet partners - Ms Rice, Russian Foreign Minister Sergei Lavrov and EU foreign policy chief Javier Solana.