As part of truce efforts, Ban was to meet with Israeli President Shimon Peres in Jerusalem on Tuesday. In Cairo, Ban said he would also travel to the West Bank to meet with Palestinian President Mahmoud Abbas.
Egypt, the traditional mediator between Israel and the Arab world, has been at the center of recent diplomatic efforts involving the U.S., Turkey, Qatar and other nations.
Israel demands an end to rocket fire from Gaza and a halt to weapons smuggling into Gaza through tunnels under the border with Egypt. It also wants international guarantees that Hamas will not rearm or use Egypt's Sinai region, which abuts both Gaza and southern Israel, to attack Israelis.
Hamas wants Israel to halt all attacks on Gaza and lift tight restrictions on trade and movement in and out of the territory that have been in place since Hamas seized Gaza by force in 2007. Israel has rejected such demands in the past.
Hamas leader Khaled Mashaal told reporters in Cairo on Monday that Hamas would only agree to a cease-fire if its demands are met. "We don't accept Israeli conditions because it is the aggressor," he said. "We want a cease-fire along with meeting our demands."
Associated Press writers Hamza Hendawi in Cairo, and Karin Laub and Ibrahim Barzak in Gaza City, Gaza Strip, contributed to this report.
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