Fleet, who works as a roofer in Rotorua, was last seen at 6pm on Monday night. He left his grandmother's house, where he was living, leaving his shoes, wallet, car and keys.
His uncle, Raymond Fleet, 51, also went missing around the same time.
Rotorua police believe the men are together and could be in the Rotorua or Auckland areas.
Rotorua Detective Sergeant George Stanton said their disappearance was at odds with their normal activities and work commitments.
Bronwyn Fleet understood a car arrived at her mother's Mamaku house when James disappeared but it was not Raymond.
"We have not heard anything else at all, no one has seen or heard from him," Fleet said.
"We are a very close family and live within five minutes of each other. We are always at each others' houses."
Her brother Ray is married with children.
Fleet said James' brothers and sisters all missed him and wanted him home.
"The youngest is nine and they are all incredibly worried about him," Fleet said.
James visited his mum's house on Saturday to see his younger siblings and watch TV show Game of Thrones with her.
"We can't think of where he might be and can't think of anyone who would want to hurt him."
"We just want him home."
Raymond Fleet is Caucasian, of thin to medium build and is 175cm tall.
He has a receding hairline, with short brown hair and a moustache. He has hazel/green eyes and has a tattoo of a bird on his back.
He usually works driving trucks. It's not known what clothes he might be wearing.
James Fleet is Caucasian, of medium build, with thick wavy dark brown shoulder-length hair.
He is 172cm tall, has hazel/grey eyes and has tattoos along his right arm of crossed rifles under a "Codys" symbol and a dragon-looking tattoo down his right forearm to his hand.
He was last seen wearing a dark coloured hoody and grey track pants.
Any sightings and or information can be directed to the Rotorua Police through Crimestoppers on 0800 555 111.
