Secretary of State Condoleezza Rice (search) scrambled her schedule Friday to add a trip to the Middle East (search) designed to nurture Israel's promised withdrawal from Gaza and part of the West Bank despite a spate of terror attacks.

With the pullout a month away, State Department spokesman Sean McCormack said, "All the parties need to make the maximum effort to see that this disengagement process is a success."

McCormack gave no precise date for Rice to meet with Israeli and Palestinian leaders, but the trip was tacked onto one to Africa she is expected to undertake next week.

"It's a potentially historic moment, and the parties should seize the opportunity to realize all the potential from this disengagement," the spokesman said, indicating Rice also wants to look beyond this summer's Israeli pullback.

McCormack said Rice would cover Senegal, Sudan, Israel and the Palestinian territories from Tuesday through July 24.

In spite of a surge of terror attacks, Israeli Prime Minister Ariel Sharon (search) remains committed to pulling all settlers and troops out of Gaza and part of the West Bank.

But Sharon has frequently made clear that he does not intend to give ground under threat of terror.

Rice's diversion to the region from Africa, where she had been considering a number of stops, was announced after a flare-up of violence that threatened an already tattered Mideast truce.

On Friday, Israeli forces killed Hamas militants in airstrikes after Palestinian fighters unleashed a deadly barrage of rockets and mortars.

Rice spoke with Israeli Defense Minister Shaul Mofaz by telephone, McCormack said. "We're closely engaged with both sides and we encourage them to take appropriate steps to restore order and calm," he said.

Rice has used telephone diplomacy in the last few days to try to keep Israel and the Palestinians on track to an orderly withdrawal and to encourage Palestinian leaders to go after terrorists.

She told Palestinian leader Mahmoud Abbas (search), while returning on her jet plane from an Asian trip Wednesday, that he must take immediate action to find and prosecute those responsible for the killing of four Israelis this week in Netanya.

Assistant Secretary of State David Welch, who was in the Middle East, backed up Rice's telephone call in a meeting Wednesday with Abbas.

"All parties need to do more," McCormack said, bracketing Israel with the Palestinians.

In Senegal, Rice and representatives of 30 African countries will discuss U.S. trade policies toward the region.

In Sudan, she will meet with a newly formed government of national unity and also visit the Darfur (search) region.