Turkey-backed Syria rebels 'just two kilometres' from IS bastion
Supporting Turkish forces were targeting the town with artillery fire and airstrikes but it had no immediate word on casualties, the London-based Syrian Observatory for Human Rights said.
"Opposition factions backed by Turkish troops are two kilometres north and northwest of the town of al-Bab," said Rami Abdel Rahman, director of the Britain-based Observatory.
"This progress is a continuation of the campaign that began with the capture of Jarablus and has seen the jihadists expelled from an area of 2,500 square kilometres along the border with Turkey," Abdel Rahman said.
Al-Bab, about 30 kilometres (20 miles) from the Turkish border, has been a key target for Ankara and its Syrian rebel allies since its campaign began on August 24.
Turkey's President Recep Tayyip Erdogan has said Ankara wants to capture al-Bab from IS and then push Kurdish-led forces from the nearby town of Manbij.
Abdel Rahman said IS forces in al-Bab were almost surrounded.
"The only route left open is the road to Raqqa that runs southeast from al-Bab through the (jihadist-held) town of Deir Hafer," he said.
"The rebel forces are advancing because of the support from the Turkish forces and IS has withdrawn from several areas without putting up a fight," he added.
Ankara launched its unprecedented cross-border operation saying it was targeting both IS but also the Kurdish People's Protection Units (YPG) militia, which has been a key opponent of the group.
Turkey considers the YPG a "terrorist" organisation, and wants to avoid the creation of a contiguous, semi-autonomous Kurdish zone along the Syrian border.
The Kurdish-led Syrian Democratic Forces are currently fighting an operation to capture Raqqa, IS's Syrian stronghold, with support from the US-led coalition against the group.
Washington's cooperation with Syrian Kurdish forces has angered Ankara, and Erdogan has said his troops and allied rebels intend to target Raqqa themselves.