WASHINGTON, 1 July 2003 — Now that Israel and the Palestinians have worked out a tentative deal to begin implementing the US-backed “road map’’ for peace, the fate of the initiative might hang on the answer to a pivotal question: What to do about Hamas?

The looming problem is that the major players in the new peace initiative provide vastly different answers. Some want to abolish the Palestinian militant group. Others want to offer it options, including a chance to transform itself and continue to provide social services to tens of thousands of Palestinians.

A proposed three-month agreement by Hamas and other major militant groups to halt attacks on Israel might only defer the issue temporarily.

“It’s enormously important how you deal with Hamas. It could be the difference between success and failure for the road map,’’ said Shibley Telhami, Brookings Institution fellow and the Anwar Sadat chair in peace and development at the University of Maryland.

Israel, backed by the United States, wants Hamas eliminated in all forms as a basic precondition for restoration of trust and the return of occupied territory. Because Hamas calls for the destruction of Israel and its replacement by a Palestinian state, the premise of Israel’s approach is that peace can be ensured only once Hamas is eradicated. For the Israelis, a cease-fire only puts off what they view as the inevitable need for either Israel or the Palestinians to crush the organization.

“The Palestinian Authority must fight terrorist organizations. It must disarm them. It must make sure that their infrastructure no longer exists,’’ Prime Minister Ariel Sharon told a joint news conference after meeting US Secretary of State Colin L. Powell June 20.

President Bush has used virtually identical language. “In order for there to be peace, Hamas must be dismantled,’’ he told reporters on Wednesday.

But the Palestinian Authority, backed by key European countries and pivotal UN members, favor a compromise that would persuade Hamas to disarm and end all forms of violence, but might allow it to continue providing a network of schools, health services, food banks, charities, youth groups and even sports programs in the West Bank and Gaza. There are no alternative services is many areas.

The Palestinian Authority and some European governments contend that, given the right incentives, Hamas can be transformed from a guerrilla organization to a political one in the same way the Palestine Liberation Organization was when it renounced terrorism and recognized the State of Israel more than a decade ago.

“The Europeans have traditionally distinguished between the terrorist wing of Hamas and the political and social wings. We don’t lump them into one group like the Americans,’’ said a senior European diplomat.

Hamas differs from other militant groups, such as Islamic Jihad and the Al Aqsa Brigade who also tentatively have agreed to suspend attacks on Israel. They have all carried out suicide bombings and other attacks against Israel that have killed almost 800 Israelis during the 33-month uprising. But Hamas also puts heavy emphasis on its social welfare and educational programs.

In a controversial form of aid, Hamas provides funds to the families of so-called “martyrs’’ who have carried out suicide bombings. But with help from funds raised abroad, its welfare branches also dole out vast sums for the unemployed — in a society with some 70 percent unemployment.

“Cutting off Hamas social services and charitable donations would almost immediately lead to a major breakdown in basic services and welfare in the Palestinian Authority. The impact would be devastating,’’ said the European diplomat.

Europeans say that could trigger deeper radicalization — at a time polls indicate that growing numbers of Palestinians question the tactics of violence in pressuring Israel.

As a result, the European Union resisted pressure from the White House at a US-EU summit in Washington Wednesday to put a freeze on all funds raised in or passing through Europe destined for Hamas social and political activities.

Bush urged European leaders “to take swift, decisive action against terror groups such as Hamas, to cut off their funding and support, as the United States has done.’’

The EU did put the military wing of Hamas on list of proscribed terrorist organizations it created last year. And the EU provides no funds for the other wings of Hamas.

But Europeans, led by France, argue that it is difficult to track and block funds that are raised in or go through their countries for other purposes.

“What would be the legal basis for blocking funds or prosecuting organizations if the money goes to humanitarian organizations?’’ asked a senior French diplomat.

Unlike earlier US-orchestrated peace efforts, the other players carry weight this time. The current “road map’’ was crafted jointly by the United States, the United Nations, the EU and Russia. And all members of the so-called quartet are important in exerting pressure on their diverse contacts to get the plan off the ground.

The United States, however, strongly argues that there is only one face of Hamas.

“The leadership takes credit for terrorism and violence, and despite whatever charitable or other social good these organizations may perform, as long as they have an organizational culture that expresses a commitment to terror and violence and a desire to destroy the State of Israel, it is a problem we have to deal with in its entirety,’’ Powell said on his recent trip to the Middle East.

But the Palestinian Authority also says it needs an incentive to ensure Hamas cooperation.

A strategy that might allow the movement to have a say in Palestinian decisionmaking if it embraces a two-state solution allowing Israel and a state of Palestine to coexist in peace is the one alternative that might entice Hamas to rethink its tactics, analysts say. In the meantime, the government of Palestinian Prime Minister Mahmoud Abbas has advocated a two-phase approach — first win a cease-fire agreement, which was achieved Friday, and if Hamas then violates the truce, move militarily against the extremists.

Some analysts concur.

“If they try to dismantle (Hamas) now, then they’re likely to fail. If all parties take the approach that a cease-fire is good and the first step in an incremental process, we have a better chance of succeeding,’’ said Telhami at the Brookings Institution.

The policy chasm over Hamas underscores the multi-dimensional challenge of addressing both Israeli security fears and political realities among Palestinians. Failure to address both has the potential eventually to derail Bush’s pledge to negotiate a final settlement by the end of 2005.

The debate over tactics also has broader implications than the fate of Hamas, regional analysts and diplomats say. It goes to the core of a more sweeping policy question about how to deal with militant groups with social and political wings that have proliferated throughout the 50-plus nations of the Islamic world over the past quarter century.

Which tactic is more effective-confrontation or engagement? The answer might be years away.

Remarked a well-placed European official, “Determining how to deal with Hamas will not be the last time we address this issue — and may not be the last time we have differences with the United States.’’