The man, 45, and four young children were in the boat when it tipped over in the Manukau Harbour at about 2pm yesterday.
Three of the children were pulled from the water and the youngest, a five-year-old, remains in a critical condition in hospital.
Several other people, including a firefighter who jumped into the water were also taken to hospital following their efforts to rescue those who fell overboard.
One woman who witnessed the incident said she heard children calling out "Help us, help us''.
Another woman jumped into the water to help.
"We saw these kids yelling out for help so that's when I jumped in the water to help. I've got three kids myself so I understand,'' the woman said.
As the family were swept westward by the current, some of them managed to grab the pylons under the old Mangere bridge next to the motorway bridge, said Senior Sergeant Ian Brenchley.
"Two members of the public have jumped into the water to assist them, so that was seven people in the water at one stage and we've recovered five of those. Police search and rescue are searching for the other two bodies,'' Senior Sergeant Brenchley said.
The secondhand dinghy had only recently been bought by the Mangere family and they were trying it out for the first time, the brother of the man who owned the boat told One News.
The firefighter was treated for suspected mild hypothermia, and then returned to the station.
Water Safety New Zealand CEO Matt Claridge told Newstalk ZB this morning that the Manukau Harbour is renowned as a good fishing spot.
"Like most good fishing spots it has fairly variable conditions. It can be quite risky,'' he said.
"The tide can move really fast and ... can be actually a fairly dangerous environment to be in.''
