Turkish president Recep Tayyip Erdogan addresses the 76th Session of the UN General Assembly on September 21, 2021 in New York. AFP
Turkey had been planning to help secure and run the airport before the hardline Islamist Taliban swift capture of the Afghan capital last month.
There were also negotiations on the subject this summer between Turkish and US officials but after the Taliban's return, Turkish troops stationed in the country pulled out.
Turkey's withdrawal alongside other NATO forces followed the end of the United States' longest military conflict last month.
The fall of Kabul shattered the plans but Turkey had been holding talks with the Taliban about the conditions under which it could help operate the airport.
"The government in Afghanistan is not inclusive, is not embracing all different factions. So long as that will be the question we won't be present in Afghanistan, but if the government shall be more inclusive, we can be there, present, as Turkey," Erdogan told American broadcaster CBS News.
"We would expect all women to be involved in every aspect of life in Afghanistan in a very active way. And whenever women become more active in every aspect of life, we can support them," he added, according to an interview transcript provided by CBS News.
Erdogan discussed Turkey's management of the airport with US President Joe Biden during their first meeting in June on the sidelines of a NATO summit in Brussels.
But relations are strained between the two presidents, with Erdogan admitting on Thursday they had "not gotten off to a good start".
One of the issues causing tensions is Turkey's purchase of a Russian missile defence system, which Washington says is a threat to the Western alliance.
Ahead of a visit to Russia on Wednesday, Erdogan indicated in the CBS News interview that Turkey would go ahead with a second purchase from Moscow.
"In the future, nobody will be able to interfere in terms of what kind of defence systems we acquire, from which country at what level," Erdogan said in response to questions about Turkey's future intentions.