A coalition member who is familiar with Mr. Khatib’s thinking and spoke on the condition of anonymity to discuss politically delicate matters said that Mr. Khatib resigned because of interference from Saudi Arabia, a key backer of the Syrian uprising. The member said that Saudi Arabia threatened to cut off financing and divide the coalition if its favored candidate for prime minister, Assad Mustafa, was not chosen. That demand enraged coalition members, who responded by quickly choosing Mr. Hitto, who was backed by Qatar and the Syrian Muslim Brotherhood, the member said.

Mustafa Sabagh, another member of the coalition, denied that the Saudis had interfered, and said that he believed that Mr. Khatib had resigned over Western countries’ conditions for supplying aid the uprising.

Mr. Khatib promised to keep working for the rebels’ cause outside official channels. “The door to freedom has opened and won’t close,” he said, “not just in the face of Syrians but in the face of all peoples.”

Another group of Syrian dissidents in exile, many of them Alawites — the same minority as Mr. Assad, his family and his inner circle — held a rare public gathering in Cairo to try to persuade more Alawites in Syria to abandon the government. One of the meeting’s aims was to dispel the widely held notion that Syrian Alawites, who make up roughly 13 percent of the Syrian population, all march in lock step with Mr. Assad.

Alawites at the conference said that the mainly Sunni opposition coalition had failed to reassure Alawites that they would be safe if Mr. Assad fell, and had done little to persuade Syria’s neighbors to shelter Alawites who decided to flee, several participants said.

Fears that the conflict in Syria would spill across borders widened Sunday when the Israeli military said that it had hit a Syrian military position. The strike came after two Israeli patrols came under fire from across the decades-old cease-fire line in the Golan Heights, the Israelis said, adding that the two patrols suffered no casualties.