The statement by the so-called quartet did not name Hamas but said a future Palestinian cabinet "should include no member who has not committed to the principles of Israel's right to exist in peace and security and an unequivocal end to violence and terrorism".
"In this regard, the quartet calls on all participants to renounce violence, recognise Israel's right to exist, and disarm."
The quartet of the United Nations, the United States, the European Union and Russia, is behind the Middle East peace plan known as the road map.
The group also urged Israel on Wednesday to work with the Palestinian Authority to ensure Palestinians in East Jerusalem can vote in next month's parliamentary elections.
Resistance group Hamas is participating in parliamentary elections for the first time and its popularity among Palestinians has grown considerably.
Opinion polls in the West Bank and Gaza show it is ahead of the ruling Fatah party led by Mahmoud Abbas, the Palestinian president, ahead of the 25 January election.
"The quartet calls on all participants to renounce violence, recognise Israel's right to exist, and disarm"
Middle East peace quartet
Israel wants to keep Hamas - which is sworn to the Jewish state's destruction - out of the election process since it has carried out bombings. Tel Aviv has said it will not negotiate with any Palestinian government that includes Hamas.
In its statement, the quartet said there is a "fundamental contradiction" between militia activities and building a democratic state.
The statement said Israel and the Palestinians should begin direct dialogue immediately to co-ordinate preparations for the election.
"Pro-active measures are essential to the movement of voters, election committee staff and materials and international observers throughout the election process as outlined in the road map," the statement said.
It said both parties should work to allow Palestinians in East Jerusalem to vote "in conformity with existing precedent".
The quartet urged the Palestinian
Authority to ensure secure polls
The Israeli government had warned that it would not allow Palestinians to vote in East Jerusalem because Hamas is participating there.
But on Monday, a senior Israeli official said that Israel was considering dropping the threatened ban.
The quartet also urged the Palestinian Authority to assure the security of polling stations and employees of its Central Election Committee.
"The quartet noted the continued importance of security in this regard, and calls on the Palestinian Authority to take immediate steps to ensure law and order, prevent terrorist attacks and dismantle the infrastructure of terrorism," the statement said.
The group called the coming elections "a positive step toward
consolidation of Palestinian democracy and the goal of a two-state solution to the Israeli-Palestinian conflict".
While commending the Palestinian Authority's invitation to international election observers, it urged the Authority to ensure the polls are "a free, fair, and open process".