A man alleged to have killed three members of his family in South Korea before fleeing to New Zealand this week has been confirmed as being a New Zealand resident.

South Korean media have reported that three members of the same family were discovered murdered, and Seoul police, Yongin Dongbu police station, are seeking the 35-year-old in connection to the deaths.

The man has not been publicly named, but the Korea Herald reported the man is wanted for the deaths of his mother, stepfather and teenage half-brother.

New Zealand police have been in contact with South Korean police, but a police spokeswoman on Saturday said no details were available on the investigation.

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Immigration New Zealand confirmed in a statement that the man was a New Zealand resident, who landed in the country on Tuesday - three days after the alleged murders.

"Immigration New Zealand (INZ) can confirm that this individual arrived in Auckland on 24 October," a Ministry of Business Innovation and Employment spokesperson said.

"He is a New Zealand resident. For legal and privacy reasons INZ can make no further comment and any further information should come from the New Zealand Police."

A police spokesperson on Friday said the matter was being treated with urgency and Interpol was alerted.

New Zealand and South Korea have an extradition treaty that was signed in 2001.

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.

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The newspaper reported the stepfather, aged 57, was found dead on Thursday at 4.05pm, in the boot of a rented vehicle parked in an apartment block carpark in Gangwon Province.