Arthur Brown was shot twice after three offenders approached him in Māngere early on Sunday, police say.
Counties Manukau CIB Detective Inspector Tofilau Faa Va'aelua said this afternoon that police investigators are continuing to appeal for public assistance.
Faa Va'aelua said three offenders approached Brown, shot him twice before running away from the scene.
He called the act "senseless act of violence that's left a newborn baby without a father."
Brown, 26, was fatally shot outside a group of shops on Vine St in Māngere just before 1am.
"Police are supporting Mr Brown's family but they are absolutely devastated", Faa Va'aelua said.
"If you have any information about what happened please contact the police."
Faa Va'aelua said those responsible for the death need to "man up" for their actions.
Brown was shot between the neck and collarbone on his left and another shot on his right shoulder.
Brown was linked to a street gang, Faa Va'aelua said, however they are not sure if a gang is linked to the incident.
Police enquiries at the scene have identified there were three offenders at least who attacked Brown, approaching him on foot.
Faa Va'aelua said there was always a concern when incidents of violence like this take part in the community and they are not sure whether the incident was a random attack or not.
He said Brown has come to the attention of police in the past, however, it was back in 2011.
He is survived by pregnant wife Atiliai Brown, who was due to give birth to their first child this week.
Arthur Brown's cousin, Geoff Brown, said told the Herald on Tuesday that the child was "holding a lot of people together" while they mourned a man described as "loving and generous" and "very caring and family oriented".
Brown said Arthur's death had hit the family hard and they were all finding strength in different ways.
"It is something you don't prepare for really," he said.
"It has hit us hard, all of us - we have family in Australia, America and Samoa - and this has affected not just us but our churches and our communities. Everyone is hurting."
Brown said Arthur and Atiliai had married in recent months and he'd never seen his cousin so happy.