Secretary of State Condoleezza Rice (search) warned Israel that Palestinians must be able to move freely between the separate territories they will eventually hold.

The Gaza Strip (search) must not become a walled enclave after Israel withdraws troops and settlers next month, Rice said. She also pressed Palestinian leaders to clamp down on militants opposed to any accommodation with Israel.

Rice headed home to Washington (search) on Sunday after three days of shuttle diplomacy in the Middle East that was intended to encourage the Israelis and Palestinians to keep working on the details of Israel's planned withdrawal.

Her visit was punctuated by violence, including a shooting on the main road connecting the Gaza Strip settlements to Israel just as Rice was leaving the region early Sunday.

Palestinian gunmen opened fire on an Israeli vehicle, killing a husband and wife and wounding four other Israelis. The Israeli army said two of the attackers were killed.

State Department spokesman Sean McCormack said the shooting "underscores the importance of the parties working individually and in cooperation to maintain an atmosphere of calm free from violence during this period prior to the withdrawal and during the Gaza disengagement."

Earlier, Rice made a brief visit to an African trade conference and to Sudan for a firsthand view of the humanitarian crisis in Darfur following what the United States calls genocide of black African villagers. The United States blames local militiamen backed by the Arab-dominated government, but Sudan's leaders deny it.

In the Middle East, Rice said the two sides were making progress, although she came away with no new commitments. Several practical issues remain unresolved less than a month before the mid-August start date for withdrawal.

One of the most difficult questions is how Israel will control its side of a long border with a Palestinian Gaza. Palestinians say they fear Israel will use worry over possible terrorism as an excuse to make travel and trade all but impossible.

Rice echoed some of that concern in remarks with Palestinian President Mahmoud Abbas. Economic development of the impoverished seaside territory is key to the success of Israeli-Palestinian peace, she said Saturday.

"That means that when the Israelis withdraw from Gaza it cannot be a sealed or isolated area, with the Palestinian people closed in after that withdrawal," Rice said.

Gaza and the separate West Bank territory must have some connection between them, Rice said.

"We are committed to openness and freedom of movement for the Palestinian people," she said.

Among other questions are what to do with the remains of Israeli houses and commercial greenhouses the settlers will leave behind.

"I think we can close many of these issues very expeditiously with enough will and perhaps a change in view here or change in view there," Rice said in the West Bank city of Ramallah, where Palestinians have their headquarters.

Israel has held the Gaza territory for three decades. Under an international blueprint for peace, the land would become part of an eventual independent Palestinian state.

The U.S. has no formal role in the Gaza pullout plan, but it has tried to help guide the process. Washington is Israel's closest ally and has been more involved than anyone outside the region in the long attempt to broker peace among Israel and its Arab neighbors.