The advance by the group in the country's turbulent north comes after 10 days of fighting pitting moderate and Islamist opposition forces against the Al-Qaeda-inspired organisation that has killed nearly 700 people.
"ISIL today seized control of the town of Al-Bab, northeast of Aleppo city, and took dozens of civilians and fighters prisoner," said Rami Abdel Rahman of the Syrian Observatory for Human Rights.
"The jihadists called via loudspeakers on the minarets of local mosques for residents to hand over their weapons because ISIL had come to apply Islamic law," he told AFP.
The two-day wave of air strikes killed 50 people, said the Observatory.
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Elsewhere in the province, the Observatory said the rebel groups battling ISIL were progressing in the town of Jarabulus, near the Turkish border.
"Overnight, fighting continued in Jarabulus between ISIL and the Islamic Front and other rebel groups, with the latter progressing," the Observatory said.
The fighting in Jarabulus had resumed after a deadline given by rebels for ISIL fighters to withdraw from the city passed without them leaving.
The Observatory said ISIL had executed 46 Islamists from the Ahrar al-Sham in an ambush in Kantari, 80 kilometres north of Raqa city.
The group also killed 14 prisoners in Homs province on Monday, the Observatory said.
Jihadist foreign fighters were widely welcomed by Syrian rebels when they first entered the conflict, but have experienced a backlash against their reported abuses of civilians and rival rebels.