The rebels said on Tuesday they had taken Qabasin, several kilometres northeast of al Bab, setting the stage for an assault on the last urban stronghold of Islamic State in the northern Aleppo countryside.
Al Bab is of particular strategic importance to Turkey because Kurdish-dominated militias have also been pursuing a drive to seize it. Ankara is determined to prevent Kurdish forces from joining up cantons they control along the Turkish border, for fear it will stoke Kurdish separatism at home.
"The Free Syrian Army [rebels], with the support of our special forces, is about 2 kilometres away and the siege is continuing as planned," Erdogan told a news conference in Ankara before departing on an official visit to Pakistan.
"There is resistance now, but I don't think it will last much longer," he said.
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Erdogan also said he was confident that the Syrian Kurdish YPG militia would withdraw east of the Euphrates River from the city of Manbij on Wednesday or Thursday, fulfilling a long-standing Turkish demand.
Turkey sent warplanes, tanks and artillery into Syria in August in support of mostly Arab and Turkmen rebels, an operation dubbed "Euphrates Shield" and meant to drive both Islamic State and Kurdish militia forces away from its border.
But Manbij was recently liberated from Islamic State by Kurdish-led forces backed by the United States. Ankara regards the YPG as a hostile force with deep ties to Kurdish militants who have fought a three-decade insurgency in Turkey.
The YPG said it was pulling out of Manbij and withdrawing east of the Euphrates, but was doing so in order to participate in the campaign to liberate the Islamic State stronghold of Raqqa, which is likely to further antagonise Ankara.
Turkey has repeatedly said that YPG fighters should not be involved in the planned Raqqa operation, arguing that the city is predominantly Arab.
US special envoy Brett McGurk described the YPG withdrawal from Manbij as a "milestone", saying on Twitter that all YPG units would depart after training local units to maintain the city's security against IS.