BEIRUT - A dual picture of Syria's rebellion is emerging: Fighters on the ground make advances, seizing territory in the south and even firing one of the heaviest mortar volleys yet into the heart of Damascus on Monday. But at the same time, the would-be opposition leadership is falling deeper into disarray.

The dichotomy underlines the difficulties as the U.S. and its allies try to shape the course of the fight to oust President Bashar Assad - and, more importantly, avert chaos in the event the regime is toppled.

As the Syrian civil war enters its third year, hopes that the perpetually fragmented opposition would coalesce to form a real leadership for the fighters on the ground seem more elusive than ever.

Instead, divisions broke out this week in the main opposition group, the Syrian National Coalition. Its head announced he was stepping down, complaining of restrictions on his work. Amid infighting, 10 other members said they were suspending their membership.

The resignation by Mouaz al-Khatib, a respected Muslim preacher seen as a uniting figure and a moderate against the rising influence of Islamic extremists among Syria's rebels, came only days after the SNC narrowly elected a little-known information technology professional from Texas to head a planned interim government as its prime minister.

In another blow, the head of the SNC's military branch, Gen. Salim Idris, said his group refused to recognize the new prime minister, Ghassan Hitto, because he lacked broad support among the opposition. Hitto was backed by the Muslim Brotherhood and the Gulf nation of Qatar; many prominent opposition figures boycotted the vote that installed him.

Amid the disarray, the coalition, largely comprising exiles, has made little mark among the hundreds of independent rebel brigades that are doing the fighting against Assad's forces. Most rebel groups still cobble together their own funding and arms, and give little more than lip-service to the authority of Idris' Office of the Chiefs of Staff.

Rebels have recently been running up successes on the ground. Fighters have been steadily gaining more ground near Syria's southern border with Jordan and Israel. In the north, they have been expanding the territory they hold, recently capturing the city of Raqqa, a series of military bases and the country's largest dam.

Rebels have also seized footholds on the edge of the heavily guarded capital and, while they have been unable to break into the city, they have used their positions for mortar barrages, trying to shake the government's grip.

On Monday, they fired off a volley of mortar shells that crashed near a landmark downtown traffic circle in the capital, killing two people and wounding several others, state TV said. It was some of the worst shelling in the heart of the city since the rebellion against Assad began in March 2011.

Such sporadic strikes on Damascus have grown more common in recent weeks and often appear to target government buildings. Most cause only material damage but spread fear in Damascus, which has so far has managed to avoid the widespread clashes.