The letter, first reported by Israeli daily Haaretz on Sunday morning, "stressed Israel's desire to continue cooperation and to strengthen the peace," an Israeli source said on condition of anonymity.

The letter was sent "in the last few days," the source added, with Haaretz reporting that it was delivered to Morsy, who ran as the candidate of the Muslim Brotherhood movement, via the Israeli embassy in Cairo.

The newspaper said the message "congratulated Morsy on his election, offered to cooperate with the new government in Cairo and expressed... hope that both parties will observe the Egyptian-Israeli peace treaty."

Netanyahu "emphasised that honouring the agreement is in the interest of both countries," the newspaper added, saying the Israeli premier had also wished Morsy good luck in his new role.

Haaretz said Israeli officials, after consulting with Washington, had decided to put off attempts to organise a phone call between Morsy and Netanyahu, but said the Israeli leader had dispatched an envoy for meetings with Egyptian security officials.

Netanyahu's letter repeated much of the content of the statement he made publicly after Morsy was officially declared the winner of Egypt's first post-uprising presidential election.

"Israel values the democratic process in Egypt and respects the results of the presidential election," he said in a statement at the time.

"Israel hopes to continue cooperation with the Egyptian government on the basis of the peace treaty," which the two countries signed in 1979.

Israel has watched warily as the Muslim Brotherhood has gained increasing power in post-uprising Egypt, concerned about the future of the cold but key peace the two neighbours have maintained since signing their peace deal.