Turkey proposed that it guard and run Kabul's airport after the United States and other NATO forces withdraw from Afghanistan, Reuters reports.
US officials say Ankara is imposing conditions which need to be resolved as their leaders prepare to meet next week.
Turkish Defence Minister Hulusi Akar said on Monday that Ankara's offer was contingent on backup from its allies, political and financial.
"We intend to stay in Afghanistan depending on conditions. Our conditions are political, financial and logistic support. If these are met, we can run at Hamid Karzai International Airport," he said.
NATO leaders will discuss Afghanistan at a summit next Monday, where Turkish President Recep Tayyip Erdogan will meet Joe Biden for the first time since the US president took office.
Last February, peace talks between the Taliban and the Afghan government were held in the Qatari capital Doha and resulted in an agreement, which Turkey declared its support for.