The security forces carried out an operation in the town of Tal Rafa’at, about 38 kilometers (23 miles) north of Aleppo, on Tuesday, killing the al-Qaeda leaders.
The government troops also killed at least 20 insurgents during clashes in a rural area near Aleppo.
Reports say the insurgents have also attacked the police department in the city.
Similar clashes have also been reported in the western city of Homs over the past few days.
Many people, including large numbers of security forces, have been killed in the turmoil in Syria that began in March 2011.
Syrian President Bashar al-Assad said on August 1 that the country is engaged in a “crucial and heroic” battle that will determine the destiny of the nation.