The diplomatic quartet seeking to implement a peace roadmap for the Middle East, comprising the US, EU, Russia and the UN, did not name Hamas but stated that "there is a fundamental contradiction between armed group and militia activities and the building of a democratic state", in a statement.
"A two-state solution to the conflict requires all participants in the democratic process to renounce violence and terror, accept Israel's right to exist, and disarm, as outlined in the roadmap," it said.
The quartet held a conference call ahead of meeting in London on Monday to plot its strategy following the Hamas win.
While it hailed the free and fair poll, it said the quartet's desire for peace and statehood remains unchanged.
Israel, struggling to take in the implications of the shock result, has made it clear it will have nothing to do with a Palestinian government that includes Hamas, a movement that has killed scores of Israelis over the past two decades.
Australian Prime Minister John Howard also urged Hamas to turn its back on violence, saying Australia could not have a meaningful relationship with a government that supports terrorism.
Preliminary results give Hamas a massive 76 of the 132 seats in the Ramallah-based parliament, with the long-dominant Fatah faction winning just 43, election commission head Hanna Nasser told a press conference.
Prime Minister Ahmed Qurie resigned immediately after conceding that the Fatah faction, founded by the late Yasser Arafat decades ago, had been defeated by a movement contesting its first ever parliamentary election.
Jubilant Hamas supporters broke into the parliament and hauled down the Palestinian flag from the roof, replacing it with a green Islamist banner as thousands of other jubilant followers took to the streets of the West Bank and Gaza in seas of green.
Later hundreds of gunmen from the Fatah movement marched in Gaza city angry at the Hamas election victory.
About 500 gunmen from al-Aqsa Martyrs Brigades, which is part of Fatah, fired rifles in the air prompting Hamas to order its members to leave the streets to avoid clashes.
Meanwhile Palestinian leader Mahmoud Abbas urged all parties to respect the result of the general election amid strong signs of unease from the United States and Europe.
Talk to Hamas: poll
An opinion poll in Israel has meanwhile found almost half of Israelis think their leaders should talk to Hamas.
Israeli acting Prime Minister Ehud Olmert ruled out any talks with a government involving Hamas.
However the survey, conducted before election results were announced, found 48 percent of those surveyed want a dialogue.