BEIRUT — Syria’s opposition plunged into disarray Sunday as its president quit and its military chief refused to recognize the newly elected prime minister of an interim government for rebel-held areas.

The moves reflected deep splits in the body the U.S. and its allies hope will emerge as the united face of the opposition and advance the fight to topple President Bashar Assad’s regime.

The missteps of the opposition’s mostly exile political leadership drew little notice inside Syria, where rebel fighters dismissed it as ineffective and pushed ahead with their offensive to gain ground near the country’s southern border with Jordan. Nearby, the Israeli military in the Golan Heights responded to fire by shooting back at targets inside Syria.

The first blow to the opposition Syrian National Coalition was the surprise resignation of its president, who said he was quitting in frustration over what he called lack of international support and constraints imposed by the body itself.

Mouaz al-Khatib, who rose to prominence as a preacher in Damascus’ most famous mosque, said in a statement posted on his Facebook page that he was making good on an earlier vow to quit if undefined “red lines” were crossed.

“I am keeping my promise today and announcing my resignation from the National Coalition so that I can work with freedom that is not available inside the official institutions,” he said.

He also blamed world powers for not offering Syria’s rebels the support they demand and complained that “international and regional parties” tried to push the Coalition toward negotiations with the Assad regime — something most members refuse.

“All that has happened to the Syrian people — from destruction of infrastructure, to the arrest of tens of thousands, to the displacement of hundreds of thousands, to other tragedies — is not enough for an international decision to allow the Syrian people to defend themselves,” the statement said.

Despite electing a new, U.S.-educated prime minister last week to head a planned interim government, the Coalition has failed to make much of a mark inside Syria, where hundreds of independent rebel brigades are fighting a civil war against Assad’s forces.

Reflecting the growing dissension over that move, the head of the Coalition’s military branch, Gen. Salim Idris, said his group refused to recognize the new prime minister because he lacked broad support among the opposition.