"He has a good set of lungs," the father, who wished to remain anonymous, told Fairfax.
"People are calling him the next Jonah Lomu, but we think he'll be a concert pianist."
The family has since asked for privacy.
Professor Wayne Cutfield, of the University of Auckland medical school's paediatric department, told the Herald the average weight of a newborn New Zealand baby hadn't changed greatly, but there had been an increase in babies at the heavier end of the scale.
Speaking generally, he said several factors have resulted in big babies being born.
Mother's with excess weight before and during pregnancy, gestational diabetes, and genetics all often played a role for "babies who are extremely large".
The latest Ministry of Health figures for birth weights of New Zealand babies show women aged 30-39 give birth to the heaviest babies on average.
Boys born to mothers in the 30-39 age bracket weigh an average of 3.49kg, while girls weigh 3.38kg.
South Canterbury mums are statistically known for producing the biggest babies in New Zealand, with boys born in the South Canterbury DHB weighing 3.59kg and girls 3.45kg.
Doctors had predicted the Wellington newborn could weigh close to 6.4kg but his eventual size surprised everyone.
It is the mother's second boy. Her first child weighed 5.4kg, Fairfax reported.
A child born in Hamilton in 2014, weighing 6.85kg, was believed to be the previous record holder.
The heaviest baby in the world weighed a little over 10kg and was born to giantess Anna Bates in 1879, according to the Guinness Book of Records.
New Zealand's biggest babies
• Average birth weight: Boys (3.46kg), girls (3.36kg).
• Mothers' age group: Less than 20 (3.34kg), 20-24 (3.39kg), 25-29 (3.43kg), 30-34 (3.44kg), 35-39 (3.44kg), 40+ (3.31kg).
• Mothers' ethnicity: Pacific peoples (3.51kg), European or other (3.47kg), Maori (3.38kg), Asian (3.22kg).
• Region by DHB: Northland (3.40kg), Waitemata (3.40kg), Auckland (3.37kg), Counties Manukau (3.40kg), Waikato (3.43kg), Lakes (3.40kg), Bay of Plenty (3.43kg), Tairawhiti (3.38kg), Hawke's Bay (3.38kg), Taranaki (3.44kg), MidCentral(3.43kg), Whanganui (3.47kg), Capital & Coast (3.41kg), Hutt Valley(3.44kg), Wairarapa (3.44kg), Nelson Marlborough (3.47kg), West Coast (3.41kg), Canterbury (3.43kg), South Canterbury (3.52kg), Southern (3.45kg).
Source: Ministry of Health statistics published October 2015.