WASHINGTON — The direct U.S. entry into Yemen’s civil war, for now a limited response to rebel missile fire on a U.S. Navy ship, risks a wider entanglement that could leave the next American president embroiled in a yet another unwanted Middle East war with broad implications for the region and beyond.

Obama administration officials from the White House, Pentagon and State Department all argued that Thursday’s cruise missile strikes on radar sites controlled by Iranian-backed Houthi rebels were strictly a self-defense measure and not an escalation in military involvement.

“These strikes are not connected to the broader conflict in Yemen,” Pentagon spokesman Peter Cook said. “We want to make crystal clear that if you threaten our forces, you threaten our ships, we will be prepared to respond, as we did in this case.”

The potential consequences of more American military action — and even possibly inaction — could affect the stability of the long-standing U.S.-Saudi relationship, maritime security in an area where Iran has shown increasing interest, and last year’s landmark nuclear deal with the Islamic republic. Any would impact the balance of power in the flashpoint region.

The U.S. is already involved in the conflict indirectly through its support of the Saudi-led coalition fighting the rebels on behalf of the Yemen government. And the willingness to move from proxy to active combatant, even in self-defense, opens the door to a greater role.

In Yemen, the administration’s actions have previously been confined to drone strikes against al-Qaida’s affiliate there and logistical support to the Saudis. Strikes against Houthi targets are the first of their kind.

It appears the Houthis lashed out at the United States with missile fire against the USS Mason in the Red Sea in retaliation.

The missile fire from the Houthis missed the American ship, but chief of naval operations Adm. John Richardson said, “Enough was enough,” and the Navy was ordered to launch five missile strikes.