JERUSALEM — Looking for a potential bright spot in the roiling upheaval of the Middle East, American and Israeli officials meeting in Jerusalem on Monday held out the hope of growing security cooperation between Israel and its Arab neighbors in the Persian Gulf.

That idea, basically unthinkable a few years ago, could be more plausible now because of widespread worry over Iran’s nuclear program, coupled with chaos in Syria and turmoil in Egypt. Even though Saudi Arabia and other gulf countries have long viewed Israel as the Arab world’s biggest adversary, the rise of threats they all share in common is creating a new urgency to find common ground, the officials said.

Emerging from meetings with his Israeli counterparts on Monday, Gen. Martin E. Dempsey, the chairman of the Joint Chiefs of Staff, said that discussions included “an outreach to other partners who may not have been willing to be partners in the past.”

He added, “What I mean is the Gulf states in particular, who heretofore may not have been as open-minded to the potential for cooperation with Israel, in any way.” While General Dempsey did not go into specifics, other American military officials said that possibilities include intelligence-sharing, joint counterterrorism exercises and perhaps looking for how Israeli and Saudi troops could jointly work on the training of Syrian opposition fighters.