A change to the treaty, which has held peace on Israel's southern border since then, would be a popular move domestically but it would also hand a victory to hardliners in Egypt.
Last week 16 Egyptian border police were killed by terrorists, who then seized their vehicles in an attempt to infiltrate the border with Israel.
Israel's Shimon Peres, in a letter to Mr Morsi soon after he was elected, noted that peace had saved the lives "of countless young people in Egypt and in Israel". He said: "Unlike war, peace is the victory of both sides."