JERUSALEM — The moderate Palestinian Arab leadership agreed under heavy American pressure today to resume peace talks with Israel, dropping a demand that Israel first reach a truce with Islamic Hamas terrorists acting as spoilers.

The announcement gave Secretary of State Rice a modest accomplishment for a brief troubleshooting mission. It left open the question of how both sides will eventually confront Hamas terrorists in charge of the 1.4 million Palestinian Arabs — nearly half the population — living in the sealed-off Gaza Strip.

“The peace process is a strategic choice and we have the intention of resuming the peace process,” the president of the Palestinian Authority, Mahmoud Abbas, said. He did not say when talks would restart, but American and other officials predicted it would be in about a week.

Ms. Rice said Mr. Abbas had assured her he will return to talks. Doing so is a political risk for Mr. Abbas, who had broken off negotiations last weekend to protest an especially deadly Israeli military incursion into Gaza. More than 120 Palestinian Arabs were killed, along with three Israelis, over a week of heightened violence.

If Israeli-Palestinian Arab talks resume as pledged it will essentially restore the precarious balance in place since President Bush announced last fall that the two sides would resume full negotiations for the first time in seven years. The talks are supposed to frame a deal for a Palestinian Arab state this year.

Israeli and West Bank Palestinian Arab negotiators had been meeting regularly, and keeping their discussions secret, before Mr. Abbas pulled out. The talks had produced nothing in public, and were undermined on the one hand by continued Israeli housing activity on land the Palestinian Arabs claim and on the other by the inability of Palestinian Arab security forces to control militants.

Earlier today, Mr. Abbas had said he would not restart negotiations until Israel declared a truce in Hamas-controlled Gaza.

Although he holds no authority in Gaza since Hamas’s violent takeover there last June, a Gaza truce could benefit Mr. Abbas. Israeli military action is so unpopular in both territories, and across the Arab world, that it undermines Mr. Abbas’s authority and makes it politically difficult for him to negotiate with Israel.

Israel and America fear that negotiations for a cease-fire would give Hamas a political legitimacy it does not deserve.

Prime Minister Olmert convened his Security Cabinet to discuss the Gaza situation. His office said the officials had pledged to continue battling Hamas while moving forward with peace talks with Mr. Abbas. Mr. Olmert did leave the door open to an unofficial truce with Hamas.

“If there is no rocket fire at Israel, there won’t be Israeli attacks on Gaza,” he told reporters.

Mr. Abbas backed down after Ms. Rice called him in alarm just before an afternoon press conference with the Israeli foreign minister, Tzipi Livni, where Ms. Rice planned to announce an agreement reached that morning to revive talks.

Gaza, and the deep Palestinian Arab leadership split it represents, hangs over the discussions. Israel and America have pinned peace hopes on Mr. Abbas’s moderate-led government in the West Bank while refusing contact with Hamas, which they call a terrorist organization. Israel has also tried to punish the militants for indiscriminate rocket attacks from Gaza into southern Israel by closing borders with Gaza and cutting utilities.

With Hamas dug in, it is unclear whether Mr. Abbas could carry through on any deal he makes with Israel. Meanwhile, the crisis over Mr. Abbas’s boycott demonstrated Hamas’s power to sabotage negotiations.

Terrorists had provoked the Israeli onslaught by escalating their rocket attacks last week, killing one Israeli civilian. Israel’s response was viewed by Palestinian Arabs and some outsiders as disproportionate, and Mr. Abbas was under huge domestic pressure to cancel talks.

The American-backed peace program is meant to offer Palestinian Arabs both in the West Bank and Gaza an alternative to Hamas — a vision of a future independent state made possible only by renouncing terrorism and coming to terms with Israel. But Hamas has established firm control in Gaza since a violent takeover from forces loyal to Mr. Abbas last June, and has withstood months of an Israeli embargo and international ostracism.

Israeli leaders are under increasing pressure to find some way to deal with Hamas — either through negotiation or a full-on military assault and re-invasion of Gaza, the once-occupied territory Israel abandoned three years ago. America, as a shepherd of the peace process, is also under pressure to acknowledge that Hamas is a political force and an integral part of any eventual solution to the Palestinian Arab problem.

Ms. Rice has long ruled out any accommodation to the terrorists, but she made an unusual acknowledgment of their importance today.

“There are enemies of peace that will always try to hold hostage the Palestinian cause and the future of the Palestinian people for their own state,” Ms. Rice said. “And Hamas, which in effect holds the people of Gaza hostage in their hands, is now trying to make the path to a Palestinian state hostage to them. We cannot permit that to happen.”

Ms. Livni, Israel’s chief negotiator for the Palestinian Arab talks, suggested her Palestinian Arab counterparts need more backbone.

“A peace negotiation, it’s not a gift that somebody gives the other. It’s a mutual interest, it’s a mutual aspiration and it’s a mutual dream of our two peoples,” Ms. Livni said. “So we need to be strong enough to face internal criticism, and it’s easy to do so when you know you are doing the right thing.”

Opinion polls show a majority of Israelis want peace but doubt that the one-year calendar is realistic. A poll last week also showed a majority favor truce talks between Israel and Hamas to stop the near-daily rocket barrage.

Ms. Rice and Ms. Livni appeared to rule out truce talks today, and laid responsibility for calm with Hamas.

“It ought to be pretty clear how calm comes about; the rocket attacks against Israel ought to stop,” Ms. Rice said. She said she is certain Hamas has the power to make that happen.