Korean Police want a "softly, softly approach" in tracking down a Korean man suspected of killing three family members in South Korea before fleeing to New Zealand, a NZ-based Korean journalist says.

Tony Keam, a former news anchor at KBS, Korea's largest television station, and who currently runs a local Korean TV station here, told the Herald he spoke to Korean police who told him they fear the man "could take his own life".

A Korean pastor said the community was in fear that a murderer could be among them.

The 35-year-old man is suspected of killing his mother, stepfather and 14-year-old half-brother before flying to New Zealand with his wife and two young daughters.

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The Herald has been given a name of the suspect, but New Zealand police would not confirm if he was the man they were looking for.

"Extradition proceedings have not been received, therefore police are not in a position to release further details at this stage," a police spokeswoman said in a statement.

"Police are continuing to make inquiries and Interpol is liaising with Korean authorities."

The spokeswoman said police are not in a position to add anything further to this statement.

Keam said the name of the man had been posted on Korean social media sites, and the man is linked to an address in the North Shore.

The suspect is believed to be a father of a 2-year-old and another who is seven months, and has been working in the health industry.

Pastor Andrew Moon, who today attended a service at Korean Immanuel Church, said the community was worried.

"We talked about it in church today," Moon said..

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"Most people know about the case and they feel scared because the murder suspect is a New Zealand permanent resident and is someone in our Korean community."

A woman, who is believed to be the first person here to name the suspect on Korean social media, would not speak to the Herald.

But she said through a friend that she was just posting information that had been passed on to her on a private chat.

The friend said the information stated that the suspect had recently bought a Black Mercedes SUV, and this has been passed on to the police.

"There were some suggestions that she has some links with the suspect, but she totally denies that," her friend said.

Yongin Donghu Police said the suspect was last spotted on CCTV footage entering the victims' apartment on October 21 at about noon and leaving about five hours later, according to a Korean Herald report.

Video showed the victims arrived home at about 2pm. Their bodies were discovered by the 55-year-old mother's sister late on Wednesday evening.

The victims suffered multiple stab wounds to their upper chests, and local police confirmed a kitchen knife thought to have been used was found next to the bodies.

The suspect had rented the car, which was found with GPS tracking, police said.

Detective Shin Dong-hyoun told the Korean Herald the suspect was found to have left for NZ on Monday afternoon, two days after the alleged murders.