Family of Connor Whitehead who was shot at Christchurch party remember 'precious boy'

The family of the Christchurch teen gunned down at a party say they are "shocked and heartbroken" by their loss.

Sixteen-year-old Connor Whitehead was slain at a teenage birthday party on Friday night.

A 32-year-old man has been arrested and charged with his murder, while another person remains on the run.

At a press conference on Tuesday, Connor's father James Whitehead, who spoke on behalf of mother Cheryl Merrin and their family, said he was "loved by everyone".

"Right now we want to remember and celebrate Connor for the amazing son, brother and friend he was," he said.

"Connor was an incredible brother to William, Cordelia and Emma and a special son to myself and Cheryl. We were and continue to be so proud of him."

Connor had dreams, he said; he loved music and planned to go to university and study law.

"We are devastated that we will not see him live his life and reach his potential," James said.

"Right now we want to focus on Connor as we organise his funeral and celebration of his life. We ask for privacy as we mourn our precious boy."

Four people have been arrested so far - one charged with Connor's murder, and three charged with being accessories after the fact.

Detective Senior Sergeant Nicola Reeves said police are "actively seeking" a fifth person, who continues to elude police.

"We know that there are people out there who are assisting this person," Det Sng Sgt Reeves said.

"The purpose of today is to appeal to that person - now is the time to come forward and speak to us."

She warned anyone helping him evade arrest would also be held to account.

Connor's family also had a message to this person: "Do the right thing and hand yourself in."