UN Secretary General Kofi Annan, speaking after a meeting of the group in London, said "all members of the future Palestinian government must be committed to non violence, recognition of Israel and acceptance of previous agreements and obligations, including the road map."
The quartet, comprising the European Union, Russia, the United States and the United Nations, is charged with trying to help steer the region to lasting peace. It met in the British capital in the wake of the victory of Hamas in Palestinian elections last week.
The success at the polls of the fundamentalist group, responsible for a string of deadly attacks on Israeli targets, has thrown the Middle East peace process into chaos.
In a communique at the end of its meeting, the quartet said: "It is inevitable that future assistance to any new government would be reviewed by donors against that government's commitment to the principles of non violence, recognition of Israel, and acceptance of previous agreements and obligations, including the road map."
US Secretary of State, Condoleezza Rice told reporters "You cannot with one hand talk about peace with Israel and on the other hand countenance suicide bombings."
Secretary Rice has met with UN chief Kofi Annan, EU foreign policy chief Javier Solana and Russian Foreign Minister Sergei Lavrov thrashing out a united response to Hamas’ unexpected victory.
The EU has warned it could cut funding to the Palestinian Authority, the bloc is its biggest donor, if a Hamas- led government refused to renounce violence or recognise Israel.
But Austrian Foreign Minister Ursula Plassnik said the Palestinian assembly was to expected to "support the formation of a government committed to a peaceful and negotiated solution of the conflict with Israel."
She did not say what would happen if the conditions were not fulfilled.
'Give Hamas time'
Some European Union ministers argued that Hamas, listed as a terrorist organisation by the United States and the EU, should be given time to comply with demands.
EU external relations commissioner Benita Ferrero-Waldner said the group should be given a month or two to decide its future course before the bloc responds.
"We have taken a very clear position, and now it is for them to react, but we have to give them some time," she told reporters.
French Foreign Minister Philippe Douste Blazy also supported a delay.
"It would be counter-productive to make threats when the government isn't formed yet,” he said.
Palestinian leader Mahmoud Abbas and Hamas have both urged the international community not to cut off funding "so that our people can stand on their own feet."