Updated

Israel and the Palestinians agreed on Sunday to demolish homes built by Jewish settlers on land that eventually would be part of a Palestinian state, U.S. Secretary of State Condoleezza Rice (search) said.

The fate of hundreds of Israeli houses in the Gaza Strip (search) has been a sticking point ahead of the planned August pullout by Israeli settlers and troops after more than three decades.

Rice spent the past two days trying to convince Israeli Prime Minister Ariel Sharon (search), Palestinian President Mahmoud Abbas and leading members of their governments to work together, and do it quickly.

"I saw committed parties on both sides that are doing the necessary planning," Rice said at a news conference in Jerusalem, where she met with Sharon on Sunday.

"The people who are engaged in this planning are working harder than you could possibly imagine to try and make it work. That's all human beings can do," Rice said before stopping in Jordan as part of a Middle East (search) tour intended to renew support for the peace process.

In the latest violation of a shaky 4-month-old cease-fire, Palestinian militants on Sunday ambushed Israeli soldiers doing construction work along the Gaza-Egypt border. One soldier died and an attacker was killed, the Israeli army said.

U.S. and Israeli officials said Israel will raze about 1,200 Israeli homes in Gaza to make way for a fresh start with high-rise apartments or other more space-saving housing. The Israeli homes are larger, and much farther apart, than typical Palestinian homes.

Demolition was the Palestinians' preference, said Israel's foreign affairs spokesman, Mark Regev. "If they wanted them they could have had them," he said.

Abbas said Palestinians will cooperate with Israel to remove the rubble and may use the debris for construction projects elsewhere in the area.

Abbas also told Israel TV that he expects to reach agreement with Israel on allowing Palestinian security forces to enter the settlements after the withdrawal. That would prevent theft and looting of other buildings or improvements the Israelis leave behind, Abbas said.

The houses are among that issues left hanging for months, either because the two sides disagreed or because they were not talking to one another. Rice was clear that many hurdles remain and promised further U.S. help.

Houses are part of the larger question of what to do with Israeli-built infrastructure in Gaza and, eventually, in the larger West Bank.

Rice indicated she favors a plan to turn over Israeli-built commercial buildings and greenhouses in Gaza. But there is no agreement on that point.

"This is not easy and the next several months ahead of us are complicated and consequential to the future," she said.

Gaza is a sliver of Mediterranean coastline that Israel seized from Egypt in 1967. The densely populated land has about 1.3 million people, including about 8,500 Jewish settlers. A proposed Palestinian state would combine Gaza with the larger West Bank area.

The pullout will be the first time Israel has withdrawn from land that Palestinians claim for a future state. Some settlers claim they are fulfilling a holy mandate, and settlements are an emotionally freighted issue even among secular Israelis.

Public opinion polls show Israeli support for the withdrawal is dropping, but Sharon said he will stay the course.

"Israel is a peace-seeking country," Sharon said before meeting with Rice. "After so many years of terror and bloodshed the achievement of security, peace and tranquility is not an easy task."

In the Jordanian capital, Rice asked for wider Arab support for the Gaza pullout plan.

"I think they will work to coordinate and make this a success, but we all have to say to any who might reject this and might try to disrupt the withdrawal — and I mean by this terrorist organizations — that it is simply unacceptable to the international community and particularly in the Arab world that the Palestinians would be denied this chance."

A government statement released after Rice met with King Abdullah II said, "The Gaza withdrawal must be a step on the road for a withdrawal from the West Bank as well."

The king told Rice it was important for the U.S. to keep pushing the peace process forward "until it achieves its true objectives," according to the statement.