The two sides held a meeting, which lasted for an hour, but did not reveal its outcome to the media.
However, sources who attended the meeting speaking to Rudaw on the condition of anonymity, said the state and Kurdish officials agreed that Kurdish Asayish forces will be tasked with the protection of the airport and state-affiliated security forces will be based in a room in the airport for coordination purposes.
All former employees will return to their jobs, according to the deal.
Rudaw spoke to two members of Asayish but they refused to comment on the meeting.
Next week, a delegation from the Syrian Civil Aviation Authority is set to visit the site to carry out renovations. Later, flights will be resumed at the airport.
Viviyan Fetah contributed to this article from Qamishli, Syria.