Israel’s government remained conspicuously quiet Thursday about the Egyptian military’s ouster of Mohamed Morsi from the country’s presidency, as Egyptians continued either celebrating or lamenting the removal of the democratically elected Muslim Brotherhood leader.

“Israel is trying to keep its distance from what is going on Egypt and not say too much, because anything it says on this issue will be used as a weapon against one side or the other,” commented Eli Shaked, who served as Israel’s ambassador to Egypt from 2003 to 2005.

“For us it does not matter if it’s the Islamists or liberals in power,” he said. “What is important is that Egypt restores law and order and that stability is returned to all of Egypt, especially in the Sinai.” The retired ambassador added, “Cairo has lost most of its sovereignty over the Sinai, and the peninsula has become a jumping board for terrorists.”

Over the past two years, Israelis have eyed the Sinai, which borders southwestern Israel, with growing concern as increasing numbers of Egyptian soldiers and civilians have been kidnapped and even killed by militant infiltrators, smugglers and bandits. Since the fall of Egyptian president Hosni Mubarak in 2011, Israel’s Foreign Ministry has warned its citizens not to visit the area, once a popular destination for Israeli tourists.

Further instability in the Sinai would only deepen Israel’s security problems as it simultaneously grapples with spillover from the civil war in Syria on its northern border and ongoing tension with West Bank Palestinians to its east.

According to Elie Podeh, a professor of Islamic and Middle Eastern studies at the Hebrew University of Jerusalem, the swing in Egypt’s leadership from Islamist to the military brings a small ray of hope that the new government might be able to reclaim the desert peninsula that sits between Israel and mainland Egypt.

“The problem is that it is not a top priority right now; first they have to deal with Cairo,” Podeh said. Speculation that ousted Muslim Brotherhood leaders and other Morsi supporters could now make their way to the lawless peninsula might become reality, he added.

“In the short term, there could be a problem in Sinai, but I hope the [Egyptian] army will make a serious attempt to retake it,” he said.

While there is cautious optimism here that a takeover of Egypt by more secular forces will benefit Israel, Podeh warned that it is still too early to tell who might emerge as Egypt’s next elected president and where the new leader’s sentiments toward Israel might lie.

“Despite all the fears, Morsi was not so bad for Israel,” he said. “From what I understand, security coordination [between Israel and Egypt] was no less good than with Mubarak, even though there were no diplomatic relations.”

In addition, Egypt’s Islamists, ideologically tied with the Hamas organization that rules Gaza, did provide a channel, albeit tenuous, between Israel and the militant Palestinian group, Podeh said. Morsi managed to broker a cease-fire between Hamas and Israel following a flare-up of violence in November. With a more secular leadership in Egypt, such a channel might no longer exist.

With Hamas perceived to be increasingly isolated in the region, the group insisted Thursday that Morsi’s downfall would have little impact in Gaza.

In the West Bank city of Ramallah, meanwhile, Palestinian Authority President Mahmoud Abbas issued a statement congratulating Adly Mansour, who was sworn in Thursday as Egypt’s interim president.