"Somebody has the answer to my dad's death," he said.
"If you know anything - anything at all, please let the police know."
He said the family had been "robbed" of Mr Wilkinson's love and while the appreciated the public focus in finding the killer and helping police, they wanted to grieve privately.
Mr Wilkinson's daughter Cory Rance and widow Luise were at the press conference but were too distraught to speak publicly.
Detective Inspector Chris Page said police were still seeking the weapon used to kill Mr Wilkinson and had widened the area they were searching. It is unclear what kind of weapon was used, he said.
CAN YOU HELP?
Information for the Operation Brad investigation could be left with police on 07 858 6200 or anonymously with Crimestoppers on 0800 555 111.
Statement from Murray Wilkinson's son, Dan Wilkinson;
"At Waihi Beach in the early hours of New Year's Day, a person unknown to us took our Father, Husband, Grandfather, Brother and worst of all, our mate!
"It is impossible to express the complete devastation our family is now going through. While we appreciate that most of you will sympathise or feel empathy for us, what we need most is to find the person or person's responsible for my Father's murder.
"We are desperate to understand who took my Dad from us and why? If you know anything, anything at all, even if you have photographs that show the crowds and what was happening in and around the area that night, please let the police know.......Somebody has the answer to my Dad's death.
"My children and my sister's children have been robbed of their grandfather's love and Lu has lost the love of her life, due to senseless, brutal violence.
"My Dad is a selfless, honest and humble man who would be horrified at the attention he is receiving. We owe it to my Dad to stop this happening to another family, so no one else has to have their life ruined like us."
