The quarrels and bickering of the two small factions within the club disturbed the majority of the members.
Damascus has also labeled as terrorist groups a pair of armed factions that are part of the opposition committee.
The Free Syrian Army has struggled despite receiving American support, while hard-line Islamist factions have become more powerful.
Shortly after the attack, Azam Tariq, a spokesman for a breakaway faction of Pakistani Taliban, claimed responsibility in a telephone call with The Associated Press.
The faction of insurgents began by faulting the previous board for financial missteps, which had endangered the agencys cash flow.