The man was tasered at the scene before being taken away in a police vehicle.
Morgan said police believe the shooter acted alone.
The Caucasian suspect is believed to have been driving a dual-cab ute.
Northern Territory Chief Minister Michael Gunner described the incident as an "incredibly hard night".
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"This many be an event you prepare for but this is never an event you want to respond to".
"This has been an incredibly hard night tonight".
Another witness said he saw the shooter walking calmly though the motel.
Witnesses recalled harrowing scenes as a man moved from room to room opening fire at a motel.
NT Police are still urging people to stay inside and said it was an active police operation.
Another witness said she helped a bleeding women "with holes all in her skin" after a boyfriend carried the victim from the same hotel.
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"I was on the phone with the police and I said "He's gone right towards The Gardens" and I just said that and the cops come and chased him that way".
He said that Police had mounted road blocks around the city, which has a population of about 136,000, to arrest the gunman.
Prime Minister Scott Morrison, who is now in London to commemorate the D-Day anniversary, told reporters the shooting is not being treated as a terrorist incident.
"This is a bad act of violence that has already I'm advised taken the lives of four people, ' he said".
Darwin is the capital of Australia's Northern Territory and a former frontier outpost.
Mr Morrison said the community in Darwin would be "rocked" by the attack, but advised it was "not a terrorist act".
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