In a report, the Crisis Group says, since the collapse of the Arab-Israeli peace process in 2000, none of the governments in the Middle East has shown willingness to compromise.
It blames the international community for a lack of resolve in trying to end the Israeli-Palestinian conflict, and calls on the United States, Europe and Arab countries to become more involved in trying to find a comprehensive settlement.
Former U.S. Ambassador to the United Nations Thomas Pickering, who is a co-chairman of the Crisis Group, says the timing of the new initiative to bring the parties back to the bargaining table is important.
"I think the Crisis Group is doing this, in part, because coming out of the really miserable conflict that we have been through over Lebanon, there was a very strong sense of thinking that there is now a time and an opportunity, as there has been after most of the conflicts in the Middle East, to direct new energy into the Arab-Israeli peace process," he said. "The need is self-evident, given all of the turmoil and problems going on in the Middle East."
Joining in the call for urgent international action, 135 global leaders, including former presidents and prime ministers, have endorsed the Crisis Group's initiative.
The plan calls for an international meeting on the issue, perhaps modeled along the lines of the Madrid Conference.
That conference, in 1991, brought together, for the first time, Israel, Syria, Lebanon, Jordan and the Palestinians for talks after the first Gulf War.
The proposal also calls for negotiations between Israeli and Palestinian leaders on the immediate issues of mutual security and revival of the Palestinian economy.
The senior vice president of the Crisis Group, Mark Schneider, says unless attempts are made to resolve the conflict, the situation in the Middle East will only get worse.
"That issue is fundamental to all of the other consequences that we have seen: the increasing radicalization within the Middle East, the increasing targeting of the United States in every possible way, and the loss of U.S. influence," he said. "There is no issue in that part of the world that does not hinge in some degree, in some way, on resolving the Arab-Israeli conflict."
The Crisis Group is also calling for an end to the international political and financial boycott of the Hamas-led Palestinian Authority, if the Palestinians form a national unity government.
Talks to form such a government have stalled, and there have been deadly clashes between armed members of Hamas and the once-dominant Fatah party.
Mark Schneider of the Crisis Group says continued Palestinian infighting makes the new peace initiative even more urgent.
"To some degree that very specter of increased violence and instability among the Palestinians, we hope, will be seen as a process that cannot be allowed to continue," he said. "That is not going to produce a stable movement towards a two-state solution, which everybody agrees is still the only, successful and likely answer to peace in the Middle East."
The United States and other countries have labeled Hamas, which has carried out numerous suicide bombings against Israelis, a terrorist organization.
Western countries cut aid to the Palestinian Authority after Hamas came to power earlier this year.
The international community has demanded that Hamas recognize Israel and renounce violence, conditions the militant group is refusing to accept.
Crisis Group co-chair Thomas Pickering says Hamas must agree to negotiations with the Jewish state.
"The message that we need to send to Hamas is, no governance without acceptance of a negotiated solution to the problem, and that is the bridge they have to cross," he said. "My feeling is, they know the bankruptcy of militancy, and, now, they have to be taught the opportunities of diplomacy."
Earlier this month, U.S. Secretary of State Condoleezza Rice met with leaders of moderate Arab states as part of a Middle East tour designed to explore ways to reinvigorate the peace process.
Former U.S. Congressman and Crisis Group board member Stephen Solarz says many Arab governments are pressing the United States to help revive negotiations.