Police have been in contact with South Korean authorities this afternoon, after it emerged a man suspected of killing his family in the Asian country is believed to have fled to New Zealand.

A police spokesman confirmed just after 5.30pm that Interpol was liaising with authorities overseas and the matter was being treated as a priority.

"However, we are unable at this time to go into specific details of steps being taken while we work to gather further information."

The wanted man is suspected of killing his mother, stepfather and 14-year-old half-brother in South Korea.

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The Korea Herald has reported that the 35-year-old murder suspect is believed to have taken a flight to New Zealand on Monday afternoon, Korean time, two days after the trio's deaths.

According to Yongin Dongbu Police investigations, the suspect was last spotted on CCTV footage entering the victims' apartment on October 21 about noon and leaving about 5pm, the Korea Herald reported.

The CCTV footage showed that the victims arrived home about 2pm, and their bodies were discovered by the 55-year-old mother's sister late on Wednesday evening.

The Korea Herald reported that the victims suffered multiple stab wounds to their upper chests and local police confirmed a kitchen knife thought to have been used in the stabbing was found next to the bodies.

Yongin Dongbu Police confirmed on Thursday afternoon that the suspect's stepfather, the husband and father of the victims, was murdered as well.

The stepfather, aged 57, was found dead on Thursday at 4.05pm, in the boot of a rented vehicle parked in a condominium carpark in Gangwon Province, the Korea Herald reported.

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

"The suspect was found to have left for New Zealand on Monday afternoon, two days after the alleged murders," Yongin Dongbu Police Station detective Shin Dong-hyoun told the Korea Herald.

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"We will request for Interpol's assistance for his extradition."

Shin declined to give further details on when the request would be made.

The two countries have an extradition treaty that was signed in 2001.