"The decision ... is ill-advised, a violation of our sovereignty and territorial integrity and against our national interests," the group said in a statement, days after Turkey promised to provide troops to protect Kabul airport when foreign forces leave next month.
Turkish President Recep Tayyip Erdogan had said on July 9 that Turkey and the US agreed on the "scope" of how to secure Kabul airport under the control of Turkish forces after Washington's withdrawal from Afghanistan.
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.
Erdogan 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 Erdogan held talks with US President Joe Biden in Brussels on the sidelines of a Nato summit in June.
However, the Taliban have opposed Ankara's proposal, saying that Turkey should also withdraw its troops in line with the 2020 deal for the pullout.
Washington hailed Ankara's "clear commitment" to playing a lead role in 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 had stated that Washington's exit from Afghanistan would complete on August 31.