Ankara launched an unprecedented incursion to support rebels inside Syria in August, making rapid advances in initial stages but has been locked in a bloody battle for Al-Bab since December.
Turkish Prime Minister Binali Yildirim said Al-Bab was now "surrounded on all sides" and the town's outer neighbourhoods were "under control".
"The efforts to take it completely under control continue," Yildirim added during a press conference in Ankara with the head of Libya's unity government Fayez al-Sarraj.
Fighting raged on the ground near Al-Bab on Wednesday as Turkish troops and allied rebels forces clashed with IS fighters, the Britain-based Syrian Observatory for Human Rights said.
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The monitor said both Turkish troops and allied rebels and Syrian regime forces had advanced towards IS-held Al-Bab overnight. Anadolu news agency said pro-Ankara forces had captured strategic hilltops from the jihadists.
Foreign Minister Mevlut Cavusoglu said that over the last few days, Turkish special forces, soldiers and Syrian rebels had made "serious" progress in Al-Bab.
"The target after this (Al-Bab) in Syria is the Raqa operation," Cavusoglu said alongside his Saudi Arabian counterpart Adel al-Jubeir in Ankara.
"As regional countries, as countries inside the (US-led) coalition, we can put our special forces in, we need to put them in," Cavusoglu added, referring to any Raqa offensive.
His comments come after US President Donald Trump and Turkish President Recep Tayyip Erdogan spoke via telephone and discussed acting together in Turkey's battle to capture Al-Bab and also over Raqa.
Last August, Ankara launched an ambitious military operation supporting Syrian opposition fighters to clear its border of IS and pushing back Syrian Kurdish militia.