"We are all encouraged. We reaffirmed our determination to work with the Palestinian leadership to support the [January 9] elections" to choose a successor to Arafat, UN chief Kofi Annan told reporters after the meeting.
"We must give them all the necessary support. There is an opportunity to... move ahead with the road map" peace plan.
"We believe the Israeli government is also ready," the secretary-general said, also referring to discussions with the Israelis to release frozen Palestinian funds.
"We will send election monitors, ensure international support to see they get the necessary budgetary support," Annan said.
The brief quartet meeting came a day after US Secretary of State Colin Powell held talks with Israeli and Palestinian leaders on his first trip to the region in 18 months, before heading to Egypt's resort of Sharm El Sheikh.
Apart from Powell and Annan, the meeting grouped Russian foreign minister Sergei Lavrov, EU foreign policy chief Javier Solana, EU external affairs commissioner Benita Ferrero-Waldner and Dutch foreign minister Bernard Bot, whose country currently holds the European Union's rotating presidency.
A road map blueprint drawn up by the quartet set a 2005 target date for Palestinian statehood but has made virtually no progress since its launch last year and the United States is now aiming for a state by 2009.
Powell on Monday hailed a "moment of opportunity" for peace in the Middle East, as Israel agreed to allow Arabs living in annexed east Jerusalem to vote in the January elections to find a successor to Arafat.
The outgoing secretary of state, who is to be replaced by national security advisor Condoleezza Rice, is on a bid to revive the peace process in the wake of Arafat's death and the reelection of US President George W. Bush.
French foreign minister Michel Barnier, also in Egypt for the conference in support of Iraq's transition process, said there was now "a possibility to write a new page" in the Middle East.
"A new Palestinian Authority is being set up... elections which we must help organize, the Israeli prime minister's commitment to withdraw from a first territory, the American determination after the election of President Bush and then our own determination, of the Europeans," he said.
Barnier was referring to Prime Minister Ariel Sharon's plan for an Israeli withdrawal from the Gaza Strip in 2005.
© 2004 Agence France-Presse