"If you see that vehicle contact police on 111. If you are confronted or approached by anyone in that vehicle, comply and do as you are asked. We don't want any heroes," Detective Inspector Scott Beard said.
Auckland Council's parks, sports and recreation manager Mace Ward said there were no security cameras in many public areas and no plans to install them any time soon.
"As a rule, we don't have CCTV in our parks and open spaces as there is too much area to cover. Cameras are usually limited to urban centres or car parks," Mr Ward said.
He said council guides working on Mt Eden were "often our eyes and ears on the spot and will help visitors when needed".
A team of detectives have interviewed the gunman's victims and collected evidence from the three crime scenes.
So far the armed man has collected a loot of wallets and phones and also a Taiwanese passport.
He first brandished his gun when he stole from a person leading a tour group at the Domain's Wintergarden Pavilion before he drove to Mt Eden where he accosted a person at the base.
He then confronted a group of Asian visitors at the summit, stealing a handbag before firing the shots when one of the group chased him.
The robberies happened between 4pm and 5pm.
Mr Beard said the tourist areas were busy at the time and photos by people in the area may be able to help.
"That's why we're relying on the public who may have taken photos to come to us with those photos. They may well show the offender," he said.
Police located five .22-calibre bullets at the scene of the robbery at the Mt Eden summit.
The offender was driving a 2010 blue Commodore SV6 with the registration GPH784, stolen from a rental company's lock-up compound near Auckland airport earlier this month.
Mr Beard said police were looking at whether there were any other unsolved crimes committed in the Auckland region.
"It could well be that there have been other people who this offender has confronted who may, for whatever reason, have not contacted police at this stage," he said.
"By all accounts this offender was very calm, knew exactly what he wanted and what he was doing and was calm in his approach. But when he was chased he presented a firearm and discharged it into the ground."
The offender was described as being of Maori appearance, about 180cm tall with short, dark, curly hair.