Suleiman, who has acted as a go-between in the negotiations between Israel and the Palestinian militants, visited Israel last week to discuss the terms of the truce, which include a complete cessation of Israeli ground operations in Gaza and an end to Palestinian rocket and terrorist attacks on Israel from the Gaza Strip.
"Israeli leaders expressed their support for and understanding of the Egyptian proposals for a truce," Egypt's official MENA news agency quoted an anonymous intelligence official as saying.
Israel said it was "ready to implement" the ceasefire as soon as Israeli leaders had been notified of the agreement of Palestinian organizations to the proposed terms, the official added.
Palestinian factions are planning to hold a meeting this week to discuss the implementation of the ceasefire agreement.
Cairo is hoping that the truce, if successful, could help the sides resolve a host of other issues, including the release of Israeli soldier Gilad Shalit, kidnapped in a cross-border raid by Palestinian militants almost two years ago, and the lifting of an economic blockade of the Gaza Strip, imposed by Israel after the radical Islamic movement Hamas seized control of Gaza in June 2007.
Shalit's release had earlier been included in the Israeli terms for a ceasefire.
Hamas is demanding the release of 450 Palestinian prisoners in exchange for Cpl Shalit. The group's leader, Khaled Meshaal, said in March that Shalit was still alive and being treated well.
Israel has so far agreed to the release of 71 Palestinian prisoners convicted of serious crimes against Israeli citizens as part of a deal for the release of Shalit.
