A family member last spoke to Thomas Phillips on Saturday night at the gathering on the family farm but there weren't any red flags.
"There was no issues raised at the time."
Waikato West area commander Inspector Will Loughrin said they had genuine concerns for their safety, while family remained anxious for their return.
"This is out of character for the family and this is day [three] so that's why you will see a significant amount of resource to bring Thomas and the kids home."
Anyone with information is asked to contact 105 and quote job number 210913/1952.
Their vehicle was found abandoned in the surf on the remote North Island west coast beach three days ago.
Asked why it took so long to report the family missing, Loughrin said family didn't realise they were missing until their vehicle was discovered in the surf by a family member at Kiritehere Beach on Sunday.
"At that point family became concerned and then approached police on Monday morning."
Loughrin said Phillips and his three children live on the family farm at Marakopa but he also owned a property in Otorohanga.
"Thomas has a house in Otorohanga which he goes between and the family home in Marakopa."
It was unclear why they were at the beach on Sunday and why the vehicle was left on the beach.
"It was right on the beach. There were waves crashing over the bonnet."
Loughrin said there were a "number of areas of interest" in their investigation including the beach but he wouldn't be drawn on as to whether there were any family court issues.
He also wouldn't comment about whether there were any items of interest found in either the car or their house, or Phillips' state of mind.
"We are working with family and friends and establishing a timeline of movement; any background we can find out which helps inform this search operation."
Phillips' family - who were well known in the area - were "naturally upset".
"Naturally they are struggling with the fact that Thomas and the kids are missing and we are supporting them through that."
He said there was no sign of foul play at this stage.
He said the sea was one area of the inquiry along with the beach itself and surrounding bush and coastline.
The search and rescue operation had seen LandSAR crews on the beach, its surrounds, as well as the Eagle helicopter and Fire and Emergency NZ staff operating drones in the air.
The Coastguard operated a fixed-wing plane.
Conditions at Marakopa had been "fairly rough" over the last couple of days and would likely be rough again tomorrow but it was hoped conditions would be settled by Thursday.
As for Marakopa itself, Loughrin said the tiny seaside settlement was very small but had bach owners as well as permanent residents.
