AFTER FIVE months of violence and political drift, there has been encouraging movement toward peace on the Israeli-Palestinian front this week. Much of it is because of Israel's prime minister, Ehud Olmert. Over the weekend Mr. Olmert agreed to a cease-fire in the Gaza Strip with Palestinian President Mahmoud Abbas, a deal Israeli governments had refused to make for the past several years. On Monday -- though a few Palestinian rockets were still falling in Israel in violation of the cease-fire -- the prime minister delivered a major speech in which he offered the release of "numerous" Palestinian prisoners, a significant reduction in controls on the movement of people and goods in Gaza and the West Bank, and a full reopening of negotiations to create a Palestinian state.

In exchange, Mr. Olmert asked for the release of Cpl. Gilad Shalit, the soldier whose abduction by Palestinian militants touched off the Middle East's summer war and spelled the end of Israel's plan to unilaterally withdraw from the West Bank. Mr. Olmert said that peace negotiations -- the first in six years -- would depend on success in Mr. Abbas's effort to form a new Palestinian government that, unlike the present administration of the Islamic Hamas movement, would recognize Israel and renounce violence. But Mr. Olmert was clear about what those talks could lead to: "an independent and viable Palestinian state, with territorial contiguity" in Gaza and the West Bank. To create that state, he said, "Israel will agree to the evacuation of many territories and communities which were established therein."

With Secretary of State Condoleezza Rice due to meet with Mr. Abbas today, it's easy to dismiss Mr. Olmert's initiative as a public relations effort aimed at helping the Bush administration gain support it desperately needs from moderate Arab governments on Iraq and Iran. Mr. Olmert took care to describe the Arab peace initiative led by Saudi Arabia, which calls for the normalization of relations with Israel as part of an Israeli-Palestinian settlement, as in part "positive"-- the first kind words an Israeli leader has had for the plan since it was proposed in 2002.

Yet whatever its strategic motive, the Olmert initiative represents a genuine opportunity for Arab governments and Mr. Abbas. The challenge for the Palestinian president, and the Arab leaders who support him, is to use Mr. Olmert's words to break the deadlock on forming a government that can release Cpl. Shalit and commit itself to a peaceful settlement. That would unlock Israel's concessions on prisoners and movement, renew frozen international aid, and allow -- at last -- discussions on a final settlement. But it will require Hamas to soften the intransigent policy of rejection it has held since taking office in March. Do Palestinians really want their own state, or an endless war of attrition against Israel? Arab and European governments that have been insisting an Israeli-Palestinian settlement is the key to stabilizing the region must now insist that Hamas answer that question.