Hamas and Islamic Jihad on Thursday rejected Egypt's call for an immediate and unconditional cease-fire with Israel, saying they would only accept the proposal if Israel stopped pursuing their members both in the West Bank and the Gaza Strip. The announcement came during a meeting of representatives of the two groups held in el-Arish with Egyptian General Intelligence chief Omar Suleiman. Earlier in the day, Suleiman met in Cairo with US Undersecretary for Near Eastern Affairs David Welch, and discussed how to bring about an Israeli-Palestinian cease-fire. Welch was sent to Cairo on Wednesday by US Secretary of State Condoleezza Rice, as Egypt became the focus of efforts to come up with some kind of "package deal" that would calm the situation in the South. Officials in Jerusalem said it was unlikely that Palestinian Authority President Mahmoud Abbas would return to negotiations with Israel until the contours of this deal were worked out. Among the elements being discussed are a cease-fire, a new arrangement on the Gaza-Egyptian border that would include a role for the PA and European Union monitors, and humanitarian assistance for the Gaza Strip. Abbas suspended talks with Israel on Sunday, and although he told Rice he would renew them, he did not give a date. The assessment in Jerusalem is that he will only return to the table after getting some kind of face-saving concession. "If he comes back to the talks now, Hamas will crucify him," one senior government official said. "He has to show that he got something in return." Hamas and Islamic Jihad made clear that the lifting of the blockade of the Gaza Strip was a precondition for a cease-fire. The two groups also appealed to Cairo to reopen its border with the Gaza Strip to allow Palestinians to travel to Egypt and other countries. A senior Hamas official said Welch came to Cairo with an Israeli offer to stop its military operations if the Palestinians halted the rocket attacks from the Gaza Strip. "The Israeli offer was relayed to us through Omar Suleiman," the Hamas official said. "We rejected it because we insist on a comprehensive and mutual cease-fire that would also include the West Bank and ending the siege of the Gaza Strip." Prime Minister Ehud Olmert's spokesman Mark Regev, however, said Israel was not negotiating with Hamas. "Israel will continue to act against the Hamas military machine in Gaza as long as there are missiles fired into Israel," he said. Olmert, at a security cabinet meeting on Wednesday, said Israel would stop shooting if the Palestinians did. "Our forces are not operating because we want to, but because we have to," he said. "If they stop shooting at our civilian population, we would not have to respond." As for Hamas's demand that Israel stop pursing its gunmen in the West Bank, Regev said Israel's military actions there were intended to save lives. He said Israel found embryonic Kassam production facilities there earlier in the year, and that if Israel had not acted, the situation would be far more explosive than it is today. "When Abbas is up to the task of dealing with the West Bank, we will stand down," Regev said. Earlier this week, the Egyptians decided to resume their efforts to reach a cease-fire between the Palestinians and Israel. The decision, according to Palestinian sources, came at the request of some Hamas leaders at the peak of this week's IDF operation in the northern Gaza Strip. "If a situation is created where Hamas stops shooting because Suleiman convinced them to do so, then there will be a de facto situation where we won't attack," one senior Israeli government official said. "This can be a de facto cease-fire; it doesn't have to be an agreement." The Hamas delegation to the talks with Suleiman was headed by Mahmoud Zahar, while the Islamic Jihad team was led by Muhammad al-Hindi. "We made it clear to the Egyptians that there won't be a cease-fire unless Israel lifts the siege [on the Gaza Strip] and stops its aggression not only in the Gaza Strip, but also in the West Bank," Hamas legislator Mushir al-Masri said. "A cease-fire must be mutual and comprehensive." Another Hamas representative, Fawzi Barhoum, said Hamas "maintained the right to defend the Palestinians in the face of the ongoing Israeli aggression." He added: "The resistance will continue as long as the aggression continues. Israel's insistence on perpetrating additional crimes justifies the continuation and legitimacy of the resistance." Khaled al-Batsh, a senior Islamic Jihad official, said his group would continue to launch attacks on Israel as long as Israel continued its "aggression" against the Palestinians. He too said any cease-fire must also include the West Bank and the lifting of the blockade. Despite the defiant statements made by Hamas and Islamic Jihad, Arab diplomatic sources in Cairo said the Egyptians were "cautiously optimistic" regarding the prospects of reaching some kind of understandings with Israel. "The Egyptians have decided to throw their full weight behind the cease-fire initiative," the sources said. "They are working very hard to persuade all sides to accept a temporary truce." According to the sources, the Egyptian government has reported "certain progress" in the talks with the Hamas and Islamic Jihad leaders. The sources revealed that secret talks had also taken place earlier this week in Cairo between the Egyptians and representatives of the two groups. Suleiman is scheduled to visit Israel next week for talks on the cease-fire initiative. According to sources close to Hamas and Islamic Jihad, the initiative calls for an end to rocket attacks on Israel. In return, Israel would halt its military operations in the Gaza Strip, reopen its borders with the Gaza Strip and ease economic sanctions imposed on the Palestinians following Hamas's rise to power in January 2006. The plan also calls for reopening the Rafah border crossing between Gaza and Sinai, but without permitting Hamas to play any role there - an idea that has been strongly dismissed by Hamas.