They say it's highly likely more women have been attacked and are asking them to come forward.
Detective Sergeant Ian McGill said there were two stages to the investigation into the man's alleged offending. The first was appealing to potential witnesses and victims to speak to police; the second was going through crime reports to see if there were any similar incidents since the man had been in the country.
"We're going back through and reviewing same or similar crimes with similar modus operandi, reviewing crimes we think may be related and then following those up," Mr McGill said.
Police were open to any tips or information from the public about the man and his activities in South Auckland or elsewhere. He has lived in Mangere and Otara.
"We know when he arrived in the country and we know when he was arrested. Now we're making a timeline of his movements in New Zealand.
"We're not limiting ourselves. We're interested in anywhere he's been while he's been in New Zealand and what he's been doing during that time. It's likely there are more than just three victims."
The man is facing one charge of rape, another of indecent assault and two of abduction. He was remanded in custody after his first appearance in the Manukau District Court to reappear on November 9.
The women described the attacker as 1.75m tall with bushy black hair, a goatee and long sideburns. He had Samoan and Chinese tattoos on his left arm and was driving a dark green four-door sedan. He had a strong Samoan accent.
Mr McGill said the three victims were traumatised by their ordeal, but he wanted to reassure the public. "The key message is that he's been identified and apprehended and is safely in custody. Police are appealing to anyone else who think they may have relevant information to contact us."
POLICE HOTLINE
* The alleged offender is described as 1.75m tall, with a strong Samoan accent, bushy black hair, a goatee, long sideburns, and Samoan and Chinese tattoos on left arm.
* He drove a dark green four-door sedan and was living in the Mangere and Otara areas until his arrest.
Please contact Detective Sergeant Ian McGill on (09) 272-5676 or Crimestoppers on 0800-555-111 with information.