TEL AVIV—Israel has watched its cold peace with Egypt turn frigid since the downfall of President Hosni Mubarak, but as Egyptians voted for a new leader this week, some Israeli officials said they believe the peace treaty between them is likely to endure no matter who wins.

In the past year, Israel has bulked up its border defense along the chaotic Sinai Peninsula, watched its multibillion-dollar natural-gas supply deal with Egypt evaporate, scaled back its embassy in Cairo after its offices were ransacked, and listened to Egyptian presidential candidates discuss tinkering with their 33-year-old peace pact.