Phillips, and his children Jayda, Maverick and Ember, have been the subject of aerial, bush and shoreline searches around the Waikato region since he failed to reappear in the Te Kuiti District Court on January 12 on a charge of making a false statement.
He and the children were officially reported as missing by family members on January 18.
In late January, police were made aware his vehicle, a ute, had been left parked on Mangatoa Rd near the Mangatoa Track.
Police said today the children's disappearance had caused their mother and family "extreme stress and anxiety".
In a fresh appeal this morning, Waikato West Area Commander Inspector Will Loughrin urged anyone with information about the quartet's possible location to come forward; that includes even if they knew of a new family group in their community - "specifically a father and three school-aged children".
"We are mindful the photos we have made public to date may now not accurately depict what Tom and the children look like," Loughrin said.
"When Tom Phillips was last seen by family in February, he had a beard and that alone will make him look considerably different than in the photos we have circulated."
The children's appearance will have also changed since they were last seen by family in January.
"They will be taller; they will have either lost baby teeth or started to get their adult teeth and will likely be wearing their hair in different styles.
They could also be using different names, Loughrin said.
"If you think you may have seen them, or know where they are, we want the opportunity to follow up that information."
Police continue to have regular contact with their extended family, with Loughrin adding: "I want to acknowledge both the children's mother and Tom's wider family who continue to be living with extreme stress and anxiety."
Phillips' three children are; Ember Nirvana Essence Phillips, 6, Maverick Rusty Callam Phillips, 7, and Jayda Jorga Jin Phillips, 9.
Loughrin said as well as wanting to hear from anyone who knew of a father and three children of similar ages arriving in their community, police also wanted to hear from anybody around the country who had seen a man and three school-aged children travelling inter-city on trains, buses or ferries, knew of three school-aged children in your community who don't appear to be attending local schools, or had experienced the theft of petrol, diesel, food or camping supplies.
The new nationwide appeal comes after extensive searches in the Waikato and nearby King Country.
"Despite a number of land and air searches, and regular discussions with community members who spend time in Marokopa's extensive bush area, we have not located any signs of the family," Loughrin said.
The latest disappearance is the second time within months in which Phillips has disappeared with his children.
Police earlier launched a major search for him and his children in September last year when his ute was found on Kiritehere Beach with water lapping at its tyres, sparking fears the family could have been washed out to sea.
Emergency service teams and members of the local community and iwi spent 17 days looking for the family before he and his children turned up at his parents' home on September 28.
They had been staying in a tent in dense bush, his family said.
Police charged him with wasting police resources.
However, Phillips then went "off the grid" again in early December.
The young children's mother and older adult half-sisters posted on Facebook soon after calling for help finding the children, saying they wanted "these poor babies back".
Phillips later missed his January court appearance where he was due to face the charge of wasting police resources. Police subsequently issued a warrant for his arrest for failing to show.
On February 9, Phillips returned to a family member's home in the middle of the night to take supplies.
He did not appear to have the children with him as they were not sighted.
Since that time there have been multiple reports of sightings - most in the Waikato region. None had panned out.
