Alan Langdon, 46, and his 6-year-old daughter, Que, sailed from the North Island town of Kawhia on December 17, police said.

Air Force, Coast Guard and other groups were conducting searches and broadcasting alerts, police said.

The child's mother, Ariane Wyler, has reportedly hired Australian child recovery specialist Col Chapman to conduct a private search.

Local media reports that the couple was in the middle of a custody disagreement and Ms Wyler had hired Mr Chapman on a previous occasion to locate Mr Langdon and Que.

Mr Chapman told Radio New Zealand that Mr Langdon, an Australian citizen with family in New Zealand, was possibly trying to make it back to Australia.

Mr Langdon was said to be an experienced sailor, but police said they had "grave" concerns for the pair's wellbeing.

Ms Wyler said she was confident that nothing had happened to her daughter.

"I am strongly convinced that they both are alive, well and safe," Ms Wyler told Fairfax Media.

"Que spent her first four and a half years of her life on a 46ft catamaran. I believe in Alan Langdon and his capabilities as a seagoing person. Now this boat is only 21ft long. It's fairly small but in some ways it's only a small version of Que's previous home.

"Our home, the boat Tiki Sanyasin, was totally destroyed during cyclone Pam on 13 March 2015. Alan, Que and I survived the storm luckily more or less unscathed. It was terrifying and we were separated during the storm.

"I sincerely hope that they are OK and oblivious to the fact that they are being searched for. My gut feeling tells me that they are further offshore to the west."

Friend and fellow Kawhia resident Mo Shuttleworth said Mr Langdon had saved his daughter's life when his boat went down in the Category 5 tropical storm that struck Vanuatu last year.

"He went underwater with the boat at the time - they were all in the boat at the time and it was sinking."

The incident took a toll on the relationship and the pair later split, he understood.

"They lived on the water and the children were born on the water as well. He was a very get up and go person."

In July, Mr Langdon and his daughter moved from Australia to Kawhia, where Langdon tinkered away on the challenge of making seaworthy the boat that he had owned for years.

Mary Smith, a woman Mr Langdon and his daughter shared a home with in Kawhia, said she hadn't heard from the pair since she said goodbye to them on December 17.

"They just sailed away on the adventure.

"We're absolutely broken - he is a very experienced sailor but we don't know what makes people tick."

Despite a close relationship, Ms Smith said Mr Langdon had not divulged the path he intended to travel with his daughter.

"He didn't tell me where he was going and he's been with me for five months - that's just him, keeping it close to his chest."

On December 17, Ms Smith walked to the Kawhia wharf where she waved the pair off. She said Langdon seemed happy and had waited for the tide to come in before taking the catamaran on its maiden voyage after the rebuild.

"Que wanted me to go with them but I said, 'no take my heart and nanny will stay here'.

"We waved to them as they went past the wharf. He was happy as he always is when he's on the water."

She said Mr Langdon was safety conscious and had promised to check in when they reached land. He had set no timeframe on the journey, she said.

"We can't communicate with him, we can't get him on the phone but the battery could be flat or the phone off, we don't know."

News of the pair's disappearance had hit locals hard, but everyone was staying positive, Ms Smith said.

She said there was nothing suspicious about the pair's disappearance.

"We're just waiting to hear that they are OK - we don't want to think about anything else other than everything is OK and we will hear soon that they are OK.

"Sailing was their lives, that's what they did."

A search was launched for the pair on Boxing Day after they were reported missing. Police said earlier they held "grave concerns for their wellbeing" and sought any sightings of the boat described as being white with blue anti-fouling paint on the hull.

On Wednesday police said aerial searches stretching from Mokau to Northland had failed to find any sign of the boat.

Detective Senior Sergeant Stephen Ambler, of Waikato police, said Mr Langdon is a confident and competent sailor and there were no immediate concerns for the pair, however police needed to establish their welfare.

Waikato police had now completed a full search of the waters in their area, Detective Senior Sergeant Ambler said, although the Auckland Maritime Unit would continue searching.

He said one caller had reported Mr Langdon may have travelled south, but there was no further information on this.

Stuff.co.nz with DPA