In breaking with the Brotherhood to protect their domestic grip on power, the Saudi rulers may have miscalculated. The Brotherhood is a regional force. Its tentacles run from North Africa through the Middle East. By removing their patronage from the Brotherhood and throwing their full support behind the Egyptian military — and other regimes bent on crushing the Brotherhood — the Saudis may be pushing the movement to become both more extreme and more sharply anti-monarchical, threatening the Islamic legitimacy of all the Arab monarchies.

In the coming years, the larger strategic challenge facing Saudi Arabia may not be Iran, as it has been, but the Brotherhood. This new rivalry could set off protracted conflicts across the region, which in turn could disturb efforts toward a Palestinian-Israeli peace, and to contain Iran’s influence.

Already, the rivalry is affecting the United States, whose policies in Iran and Syria drew open criticism from Saudi officials last week. That criticism played to general Arab frustration with Washington, of course, but in the background was continuing Saudi resentment that Washington helped push out Mr. Mubarak in 2011, and that it now refuses to welcome the coup and the Egyptian military’s repression of the Brotherhood.

Still, there are things America could do to lessen the harm being done by the rift.

The key would be to stop ignoring Egypt, to help build its economy and to end its corrosive political impasse. Only America can rally an international effort to address Egypt’s vast economic needs, and it should use that leverage to persuade Egypt’s rulers to convincingly point the way to democratic rule. Equally important would be more American attention to Morocco, Tunisia and Jordan, where willing elements of the Muslim Brotherhood might be included in broad-based coalitions with secular democrats.

In the long run, establishing economic progress and political stability in all of those countries would be the best way to address Saudi fears that instability would spread to the monarchies. And that would do much to lessen the impact of Egypt’s current agonies on the whole region.

Vali R. Nasr is the dean of the Johns Hopkins School of Advanced International Studies.

INTERNATIONAL NEW YORK TIMES