Turkey promised to provide security for the airport once the troops leave next month, in a move hailed as an example of improved relations between Ankara and Washington.
Erdoğan said the issue was discussed between Turkish and American defence ministers on Thursday, adding: "During discussions with America and NATO, we decided on what would be the scope of the mission, what we would accept and not accept."
Turkey's move comes after Erdoğan held talks with US President Joe Biden in Brussels on the sidelines of a NATO summit in June.
Washington hailed Ankara's "clear commitment" to playing a lead role on securing the Hamid Karzai International Airport after the leaders' discussions.
The dialogue between the NATO allies continued to cement the details of the future Turkish mission with a visit to Turkey by a US delegation last month and multiple phone calls between Turkish Defence Minister Hulusi Akar and Pentagon chief Lloyd Austin.
Kabul Airport is the main exit route for Western diplomats and aid workers.
The concern is that following the US withdrawal, the airport will fall into the hands of the Taliban, so NATO is keen to quickly find a solution.
Turkey has been an important actor in Afghanistan since 2001 and deployed hundreds of Turkish military forces.
Biden said on Thursday that Washington's exit from Afghanistan would be complete on August 31, nearly 20 years after the military mission began.
He added it was "not inevitable" that the country would fall to the emboldened Taliban.
But hours after Biden's speech, the Taliban said it captured Islam Qala, Afghanistan's most important border crossing with Iran and controlled 85 percent of Afghan territory.
