Witnesses told police the man was in a group of other males at about 10.30am when he was seen with the rifle.
The weapon was described as a .303 bolt-action military rifle, with ammunition capable of being fired. The firearm was unregistered.
Police officers approached the residence and spoke to a number of people. They discovered the offender had left the area leaving the firearm behind.
Attending officers seized the rifle and launched the operation to find the man.
He was found within a short time and apprehended at another location.
Police Commissioner Maara Tetava told the CI News the man was being questioned and would likely face charges relating to serious gun offences.
The man was refused bail and will appear today before the Cook Island’s High Court.
Tetava said: “I have concerns about the lack of care regarding firearms within our community.
“Had it not been for a concerned and law-abiding member of the community, the consequences of this matter could have been very different.
“It is timely to remind the community - yet again - about the Gun Amnesty and this is a prime reason why the programme is in existence. “
The commissioner said police were investigating the legality of the firearm, which they knew had been registered some years ago.
“To have another incident when the Review Report on the tragedy of October 2016 is about to be released, reflects badly on our community.” - RM/ CIPS