Jerusalem, Israel, Feb. 3 (UPI) -- The Egyptian and Palestinian presidents, Jordan´s king and Israel´s prime minister have agreed to meet next Tuesday to try and strengthen the peace process that began to show rays of hope.

Egyptian President Hosni Mubarak initiated the summit that will be held in Sharm el-Sheikh, in the southern tip of the Sinai Peninsula.

It appeared to be a surprise move. Tuesday, a secretary to the Egyptian chief of Intelligence Gen. Omar Suleiman phoned the Israelis and reportedly said he would like to see Prime Minister Ariel Sharon. Sharon agreed.

In a brief meeting Wednesday morning, Suleiman presented the invitation. According to Channel 2 TV Suleiman offered bait: Mubarak would send a new ambassador to Israel. Egypt recalled its ambassador in November 2000, two months after the intifada began.

Sharon accepted Mubarak´s invitation.

Palestinian President Mahmoud Abbas, also known as Abu Mazen, who was in Ankara Wednesday and Prime Minister Ahmad Qureia, in Ramallah, announced their acceptance.

Thus a Sharon-Abbas meeting expected in Jerusalem, next week, turned into a full-fledged one-day summit with Mubarak and Jordan´s King Abdullah offering their help.

The previous summit, with U.S. President George Bush, Abdullah, Sharon and Abbas (who was then prime minister), was held in Aqaba in June 2003. It had a short-lived effect. Palestinian militants and Israeli troops returned to a cycle of violence and Palestinian President Yasser Arafat undermined Abbas who resigned.

Now Arafat is dead. Abu Mazen, who for years argued against armed conflict with Israel, won the presidential elections and moved to stop violence and curb anti-Israeli incitement.

Israeli Defense Minister Shaul Mofaz Sunday told the Cabinet Palestinian attacks dropped by 70 percent to 75 percent.

A Palestinian girl´s death by a gunshot Monday prompted fresh attacks on Israeli settlements and soldiers, though Israel denied troops had shot the girl. (Wednesday Palestinians fired at the Rafiah-Yam settlement, at an army post near Gadid and a woman tried to smuggle guns in a box of apples, the army spokesman said.)

Army officers, who briefed Mofaz during a visit to Gaza, Wednesday, reported "good intentions and coordination" with their Palestinian counterparts, a Channel 2 TV reporter who accompanied Mofaz said.

In a sign of the new times, Mofaz told soldiers not to let down their guard.

"The reality is very fragile, it requires you to be alert for any changing reality up to a complete turnabout," he said.

Israeli officials realized Abu Mazen needs time. "Whoever thinks that in one month he can dismantle Hamas´ infrastructure is presenting demands aimed at torpedoing the entire process," Minister without Portfolio Haim Ramon, a Labor dove said.

Developments in Israel are also conducive to an agreement. Sharon demonstrated his determination to withdraw, even unilaterally, from the Gaza Strip and parts of the northern West Bank. He has changed his coalition partners to have his way. The pullback is scheduled for this summer.

The summit could help Sharon, domestically, showing Israelis fruits of the new atmosphere. Talks about a coordinated pullback might help persuade the orthodox Shas Party to join his coalition.

The Israelis say they want to also help Abu Mazen.

One source, who spoke to United Press International on condition of anonymity, said the Palestinian´s president faces "powerful elements" of the Hamas and the Islamic Jihad who are armed.

Egyptian, Jordanian and perhaps Saudi Arabian backing for Abu Mazen would strengthen him, the source said.

"We are calling for international support to provide an atmosphere which would held help Abu Mazen make his choices," the Israeli Foreign Ministry´s spokesman Mark Regev told UPI.

"If significant players in the Arab world are going to give diplomatic support to the Palestinian Authority to take the right steps that is obviously a good thing," Regev added.

A ministerial committee is scheduled Thursday to consider confidence- building measures Israel would take.

They will consider releasing hundreds of Palestinian prisoners. Haaretz talked of 500 prisoners.

"Such a unilateral step would be a right move, at this moment," Ramon said.

But Abu Mazen is reportedly seeking the release 8,000 prisoners, almost all the security prisoners Israel has.

Abu Mazen wants Israel to withdraw to the pre-intifada lines. That would restore complete Palestinian jurisdiction over 17.2 percent of the West Bank and civilian responsibility over 23.8 percent more, according to the Palestinian Academic Society for the Study of International Affairs.

Israeli officials are advocating a step-by-step approach, one city at a time, depending on the Palestinians´ ability to control them. Those cities would be Jericho, Bethlehem, Ramallah, Qalqilya and Tulkarim.

"Only when they will be really ready, able to promise no terror would emerge there (should Israel move out). ... Do it at the right pace, slowly, that they should only assume tasks they can meet," Ramon said.

Prime Minister Qureia told reporters in Ramallah he would seek "a mutual cease-fire agreement." Israel has avoided that, declaring that if the Palestinians were quiet, it would be quiet too.

And while the Palestinians want to begin implementing additional clauses in the internationally backed "roadmap" for peace, the Israelis say: First provide security.

One of the elements in the "roadmap" calls for a freeze on settlement activity.

Peace Now´s settlement monitor Dror Etkes, Wednesday showed reporters aerial photos with the results of extensive development in West Bank "outposts." Some sites contain permanent houses with red-tiled roofs, roads and services.

So while the Palestinians seek a political element in the talks, Sharon, according to government officials, wants to discuss security matters only.

"Yes we´ve agreed to the ´roadmap,´" Regev said, but noted it stresses security matters must be handled first. "Stage one (must be completed) first and there is no skipping the stages," Regev stressed.

Other issues require Egyptian cooperation.

Sharon would like to withdraw from the entire Gaza Strip including the Israeli wedge separating the Palestinian area from Egypt, known as the Philadelphi route. Palestinians have been smuggling weapons there and if the Israelis leave, with no security arrangements in place, Palestinians, the Israeli government fears, could bring more lethal weapons into the Gaza Strip.

Israel wants Egypt to upgrade its supervision near the border and deep in the Sinai Peninsula.

"When the Palestinians will act with determination, prevent arms smuggling from the Sinai ... if we will be convinced Philadelphi is ... first and foremost under Egyptian supervision, we´ll get out," Ramon said.

Mubarak and Sharon´s relations have been strained for years, but there has been a thaw in recent months after the Egyptian leader told reporters Sharon "could move on the peace track and produce a solution, if he wants to do so."

Regev noted that, "Over the last few weeks, there has been a substantial improvement in the climate of relations between the Egyptians and Israel."

The Egyptians are expected to send better troops to the border area and to train Palestinian policemen. Israel asked Jordan, too, to train Palestinian policemen.

"The Egyptians are vital for the peace process with the Palestinians," Ramon said. They have always tried to moderate the Palestinians. Their role is especially important in Gaza that security-wise, from the Egyptian security perspective, "Is their back yard when Israel is not there.

"Only the Egyptians can guarantee there would be no smuggling. Only the Egyptians can exercise strong and perceptible influence over Hamas ... and ... ensure quiet after we leave Gaza. ... The summit is good," he added. (Copyright 2005 United Press International 02/03/05)