Hamas officials said on Wednesdasy that they have rejected Israeli conditions for a tahadiyeh (cease-fire), which include freeing kidnapped St.-Sgt. Gilad Schalit. Prime Minister Ehud Olmert told US Middle East envoy George Mitchell on Wednesday that while the Gaza crossings were open that day for humanitarian aid, their full, routine, permanent functioning would require a solution to the Schalit issue. Olmert has reportedly offered to gradually open the border crossings in exchange for Schalit, who was kidnapped near Gaza in June 2006. A spokesman for the Prime Minister's Office would not confirm the report. Syrian-based Hamas leader Khaled Mashaal said Hamas will not accept a deal in which Israel would open the border crossings with the Gaza Strip only after guaranteeing Schalit's release. "In response to Olmert, the child killer," Mashaal said Wednesday during a speech aired by al-Jazeera. "I say to you in the name of Hamas and in the name of the heroes who are holding Schalit, we will not accept that the crossings be opened in exchange for Schalit." Salah el-Bardawil, a member of the Hamas delegation currently in Cairo, also reiterated on Wednesday that it was not possible to link the truce to the release of Schalit, and said that if Israel wanted him it had to pay the appropriate price. "We said clearly that we have our vision and a list that we presented to Egypt, and the ball is in the Israeli court," Bardawil told Al-Jazeera from Cairo. "If they want to release Schalit, they have to pay a price in return... the 11,000 Palestinian prisoners in Israeli jails waiting to be released." Since the end of Operation Cast Lead, Hamas has refused to connect the Schalit issue with reopening the crossing points and reaching a truce. Hamas has restated this position with the Egyptians at every meeting, saying that Schalit's release depended on the release of a list of security prisoners it submitted to Ofer Dekel, Prime Minister Ehud Olmert's former coordinator on the Schalit issue, some time ago. Earlier on Wednesday, an Egyptian Foreign Ministry spokesman said Tuesday's violence near and inside the Gaza Strip was not expected to disrupt efforts to secure a long-term truce between Israel and Hamas. "I don't think it will affect the diplomatic efforts very much," Hossam Zaki told The Jerusalem Post. "We have an objective to achieve. I think the two parties have already taken the political decision to enter into a period of calm, and I hope this incident will not affect the situation as a whole." An IDF warrant officer - a Beduin scout whose family does want his name published - was killed and another soldier was seriously wounded on Tuesday by a bomb that exploded inside the Gaza security fence as their patrol passed just outside the fence near the Kissufim crossing. It was the first lethal attack by Palestinians since Israel withdrew from Gaza last week. Four other bombs failed to explode. Zaki described the current negotiations, which are being brokered by Egypt and include discussions of a long-term truce between Israel and Hamas, as "positive." Hamas has been pushing for the opening of all crossing points into the Gaza Strip and for all construction materials, such as cement, iron and steel, to be allowed in. Hamas is now willing to accept the presence of Palestinian Authority officials and monitors from the EU Border Assistance Mission at Rafah, and Turkish monitors at any of the crossing, another Egyptian official said. Hamas has also demanded that European observers live either in Gaza or in Egypt rather than in Israel, so that Israeli defense officials cannot prevent them from entering to monitor the crossing, the official said. The EU Border Assistance Mission members currently live in Ashkelon, and they have not monitored the border since they left it for fear of Hamas attacks. Today, the Egyptians control the Egyptian side of Rafah while Hamas controls the Palestinian side of the crossing. Zaki also dismissed claims on Wednesday that Egypt is concerned that a deal between Israel and Hamas will not be struck before the Israeli elections on February 10, which Likud's Binyamin Netanyahu is favored to win. Netanyahu on Tuesday responded to the bomb attack near Kissufim, saying during at a Likud election campaign event: "Sooner or later, we'll need to finish the job in Gaza, and that we will do." Zaki said Egypt did not concern itself with Israel's internal affairs. "It is up to Israeli citizens to elect whoever the want," he said. "We have dealt in the past with all prime ministers and we will continue to do so." Expanding on statements made by Egyptian Foreign Minister Ahmed Aboul Gheit on Tuesday, Zaki said it was "puzzling" that ships from Western countries would rush to send ships to guard the coast of Gaza. France has already sent ships to Gaza's coastal waters in an effort to stop arms smuggling, Zaki said. Britain and Germany had previously offered to do the same. "If such ships rush to guard the coast against whatever... before reaching an agreement that would open and allow crossings to function normally and for the blockade to be lifted, those ships would enhance the perception (in the Arab world) that Gaza is effectively under siege, not only by Israel but with the help of Europe," he said. "It's a very negative and invasive feeling." AP contributed to this report.