ACT Police said while many witness statements have been taken, investigators believe there are people who were in and around the check-in area at the time who have not spoken to police.
The terminal was evacuated at about 1.30pm last Sunday, when a man reportedly fired about five shots towards glass windows.
Police said no shots were directed toward any passengers, staff or other people.
No one was injured during the incident but the airport was evacuated and remained closed for about three hours.
Officers are asking anyone who had family members or friends who used the airport early Sunday afternoon and who witnessed any suspicious behaviour to contact police if they have not already done so.
A similar call is being put out to any interstate travellers who used the airport around that time.
He will remain in custody until the case returns to court on September 5.