A suicide bus bombing in Jerusalem killed 20 people on Tuesday and shattered the relative calm that has accompanied a cease-fire between Israel and Palestinian militant groups. It also imperiled the fragile peace process.

Rather than immediately bomb the hideouts of Hamas functionaries as it has done after previous suicide bombings, the government of Prime Minister Ariel Sharon agreed to hold off retaliatory attacks to give the Palestinian government time to root out terrorist organizations such as Hamas and Islamic Jihad on its own. Unfortunately, Prime Minister Sharon’s government held off only for a day before a top Hamas official was killed in a missile attack on his car. That clearly was not enough time for Palestinian Prime Minister Mahmoud Abbas and his government to arrest those responsible as he pledged he would do.

But would there ever have been enough time? Both Israel and the Palestinians have made much progress toward peace guided by the American-crafted “road map.” The Palestinians dumped Yasser Arafat in favor of Mr. Abbas, although the United States is contemplating bringing Mr. Arafat back into the process because he has more control over terrorist groups than Mr. Abbas. The Israelis freed prisoners and tore down settlement outposts and border checkpoints. Both parties adhered to a cease-fire for nearly two months. Then came the worst terrorist attack in years.

It is too early to abandon the road map. U.S. diplomats must still remember the work and progress of Prime Minister Yitzhak Rabin’s disengagement agreements with Egypt and Syria in 1974, followed by an agreement with Egypt the next year. Mr. Rabin showed that peaceful change was possible; his assassination in 1995 at a peace rally showed the destructiveness of extremism, including from within.

With some notable exceptions, such as the continued construction by the Israelis of a barrier in the West Bank, both the Israelis and Palestinians have made large strides toward peace. The problem remains finding ways to mollify groups that thrive on undermining the peace process. In the end, there must be a Palestinian state, but Israelis are right to want assurances that it does not become a safe haven for those plotting to kill them. Once such a state is established, the hope is that young Islamic militants will see that having a job and a say in their government is more productive than killing themselves in suicide missions. The seemingly impossible task now at hand is making that transition.

Some, including Martin Indyk, a Middle East policy expert at the Brookings Institution, have suggested a Palestinian state that is run as an international protectorate whereby an arbiter (writing in The New York Times, he suggests the United States) would ensure that both groups do what they have pledged. This is a good model, but clearly the United States has its hands full with troops involved in peacekeeping in Iraq and Afghanistan. The United States should not abandon its valiant attempts at peace, but it is time for other countries and institutions to try to break the cycle of violence in the Middle East.