The 28-year-old died in Greenwood Rd, Māngere, on Tuesday morning after being shot "more than once", police said.
A 25-year-old woman was found seriously injured at his side, also with gunshot wounds.
Tu'uheava's brother-in-law said it was a shock and his wife had been distraught since hearing of her brother's death
The shock had been even more profound because they had not realised Tu'uheava was in Auckland.
"We thought he was in Australia," the brother-in-law said.
Tu'uheava, 28, was a member of the Tongan church based in Favona Rd.
Friends and family have taken to social media to pay tribute to Tu'uheava, though the police have yet to officially confirm the identity of the dead man.
"Man this is so sad!! RIP Abraham. All my love & prayers of comfort are going out to u & ur family," Tiyana Faimafili Schwenke said on Facebook.
Brother Epalahame Tu'uheava," Anamanu Taufa said in another post.
Tu'uheava was found dead in a paddock in a light industrial area in Māngere which was known as a rough area where homeless people sleep and rubbish was dumped.
Emergency services found him and the woman about 6am on Tuesday and the woman was rushed to hospital, Detective Inspector Faa Va'aelu said.
Police launched a homicide investigation and said they were hunting for two Tongan men.
Tongan Advisory Council chairman Melino Maka said he was "annoyed" with that police description.
"They should have said they have strong leads and are looking for Pacific Islander suspects, or are all Tongan males a suspect?" he said.
Māngere MP Aupito William Sio said it was heart-wrenching to hear a young father has been killed.
"Nobody wants anyone killed in our neighbourhood. The community works really hard to promote the positive aspects of Māngere," he said.
"The reports I am seeing on social media raise serious concerns that it could be gang- or drug-related and I would like for all our community to cooperate and send that information to the police.
"I want the culprits to be found as soon as possible," he said.
A friend of Tu'uheava said the shooting was gang-related. Throughout Tuesday, patched members of a gang had driven past the police cordon at Greenwood Rd.
The injured woman was helping police piece together what happened.
Her identity is still unknown.