The Palestinians want the conference to produce an outline for a peace deal; the Israelis want more vague declarations.
The UN, US, EU and Russia met behind closed doors on Sunday at the United Nations in New York, seeking to revive the stalled road map for Middle East peace and a Palestinian state.
The group expressed optimism that progress could be made with a new road map and backed bilateral talks between the Israeli prime minister and the Palestinian president.
It also called on Israel to keep fuel and electricity services flowing to the Hamas-run Gaza Strip after Israel declared the area an "enemy entity" and said it would reduce fuel and power supplies in response to rocket attacks by Palestinians.
Tony Blair, the former British prime minister, now the Quartet's envoy, said one of the aims by the end of the year was to get a sense of what a Palestinian state could look like in terms of institutions and governance.
Invite for Syria
Rice would not say unequivocally that Syria would be invited, saying invitations had not been issued yet but "we would hope that the invitations would include the members of the Arab follow-up committee ... charged by the Arab League with following up with the international community on an Arab Peace Initiative" which offers peace with Israel in exchange for land.
The committee members are Algeria, Bahrain, Egypt, Jordan, Lebanon, Morocco, Qatar, Saudi Arabia, Sudan, Syria, Tunisia and Yemen.
Only two, Egypt and Jordan, have peace deals with Israel and Syria and Saudi Arabia remain technically at war with it.
Rice suggested that attending the US conference, expected to be held in the Washington area in November, came with some strings.
"Coming to this meeting also brings with it certain responsibilities," Rice told reporters at a news conference after the Quartet meeting.
"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."