Prime Minister Benjamin Netanyahu and President Shimon Peres both spoke with Abdel Fattah al-Sisi on Friday to congratulate him on his victory in Egyptian presidential elections and to stress the importance of bilateral ties.
The separate phone calls came two days before Sisi was due to be installed in office following his comprehensive ballot-box win last month.
Neither Netanyahu nor Peres spoke with the previous Egyptian head of state, the Muslim Brotherhood leader Mohamed Mursi, who was toppled from power last year by Sisi following street protests.
"Prime Minister Netanyahu noted to the Egyptian president-elect the strategic importance of ties between the countries and in sustaining the peace accords between them," the Israeli leader's office said in a statement.
In his phone call to the Egyptian President, President Peres wished the Egyptian people prosperity and success and expressed his hope that President Sisi will lead Egypt to great achievements.
Peres's office said that at the end of their conversation: "President Sisi thanked President Peres for his warm words."
Egypt and Israel signed a historic peace treaty in 1979, an accord seen by the West as a cornerstone of regional stability in the Middle East.
Although Mursi never threatened to renounce the treaty, Israeli officials were relieved to see an end to his Muslim Brotherhood rule and say that security along the shared border in the Sinai has improved markedly over the past year.
"Israel is committed to maintain the peace treaty between Israel and Egypt and to strengthening the cooperation between our nations," Peres's office said.
It was not immediately clear if any Israelis would be invited to Sisi's inauguration. The new Israeli ambassador has not yet presented his diplomatic credentials in Cairo, meaning that he has not been handed an invitation, officials said.