Israeli Prime Minister Benjamin Netanyahu has sent a letter to Egypt's newly-elected President Mohamed Morsi, urging him to uphold a peace treaty between the two countries, a source told AFP on Sunday.

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 Morsi, who ran as the candidate of the Muslim Brotherhood movement, via the Israeli embassy in Cairo.

Israeli President Shimon Peres, a Nobel peace laureate, sent Morsi a message of his own on Sunday, his office said, in which he wrote that "contrary to war, peace is the victory of both sides."

Congratulating Morsi on his election, Peres also expressed hope "for continued cooperation with you, based upon the peace accords signed between us more than three decades ago and which we are committed to preserve and develop for future generations of both our people."

Haaretz said that Netanyahu in his message "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 Morsi 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 Morsi 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 a statement he made publicly after Morsi 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 the 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.