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 US 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 Golan Heights responded to fire by shooting back at targets inside Syria. The military said soldiers on patrol there were fired upon and responded by firing back. It did not say if the Syrian fire was from rebels or the government.
Rebels have been making gains on the Syrian side of Golan Heights, a strategic plateau that Israel captured from Syria in the 1967 Mideast war and later annexed.
The first blow to the opposition Syrian National Coalition on Sunday 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’s 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, US-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, General Salim Idris, said his group refused to recognize the new prime minister, a little-known information technology professional from Texas, because he lacked broad support among the opposition.
‘‘For the purpose of giving power to a prime minister to unite the revolutionary forces and lead the Syrian revolution toward certain victory, we unequivocally declare that the Free Syrian Army . . . conditions its support and cooperation on the achievement of a political agreement on the name of a prime minister,’’ Idris said in an online video.
An aide to Idris, Louay Almokdad, said many prominent Syrian opposition figures opposed the election of Ghassan Hitto, who received 35 out of 48 votes cast by the coalition’s 63 active members.
While Khatib’s resignation surprised many coalition members, some said it reflected problems that have caused five other members to resign in the past week.
Coalition member Rima Fleihan said in Cairo that the body did not accurately represent Syrians.
Another recently resigned member, Walid al-Bunni, accused the Gulf state of Qatar, which heavily finances the opposition, of using pressure to install its candidate for prime minister. Others have accused the Muslim Brotherhood of exercising outsized influence.
Late Sunday, the coalition distributed a statement saying it had rejected the resignation and asked Khatib to keep doing his job.
In a small victory for the opposition, senior Arab diplomats said they would transfer Syria’s seat at the Arab League to the coalition. The Syrian government’s membership was suspended earlier in the crisis. The coalition said it would send a delegation to a league summit that begins Tuesday in Qatar.
The Syrian government, which contends the civil war is an international conspiracy being carried out by terrorists to weaken Syria, did not comment on the coalition developments. Instead, it hosted a ‘‘National Dialogue Forum’’ in Damascus that included none of the forces seeking Assad’s ouster.