Growing tensions between Saudi Arabia and Iran have raised hopes in Israel that officials can build closer ties with the Gulf monarchies based on their shared animosity toward Tehran.

Led by Dore Gold, director-general of the foreign ministry, Israel has stepped up efforts to mend and improve ties in the region—all in a bid to counter Iranian influence and the threat of Islamic extremism.

A long-standing hawkish ally of Prime Minister Benjamin Netanyahu, Mr. Gold said Israel and Sunni Arab states face a shared threat in Iran.

“Clearly there’s been a convergence of interests between Israel and many Sunni Arab states given the fact that they both face identical challenges in the region,” Mr. Gold told The Wall Street Journal.

The recent torching of the Saudi Arabian Embassy in Tehran—and diplomatic fallout between the Persian nation and Arab Gulf states—have underlined how common ground appears to be growing.