South Korean police on Thursday announced the arrest of a 42-year-old woman accused of murdering two children whose remains were found in suitcases in New Zealand.

The woman, who is believed to be the mother of the two dead young children, was arrested in South Korea on murder charges following a request from New Zealand, police in both countries said.

She will now face extradition proceedings, they added.

"Police arrested the suspect at an apartment in Ulsan on Thursday following a stakeout with tips on her whereabouts and CCTV footage," Seoul's National Police Agency said in a statement.

"The suspect is accused by the New Zealand police of having murdered two of her children, aged seven and 10 then, in around 2018 in the Auckland area," it said.

"She's been found to have arrived in South Korea after the crime and has been in hiding ever since," it added.

The Yonhap News Agency reported that the woman was a South Korean-born New Zealand citizen.

"Police plan to transfer the woman to the Seoul Central District Prosecutors Office in preparation for an extradition screening by the Seoul High Court," Yonhap said.

The grisly discovery came after an unsuspecting family bought a trailer-load of items — including the suitcases — at an auction for abandoned goods near Auckland, New Zealand's biggest city.

Detective Inspector Tofilau Fa'amanuia Vaaelua in Auckland said the case was "a very challenging investigation".

"To have someone in custody overseas within such a short period of time has all been down to the assistance of the Korean authorities and the coordination by our New Zealand Police Interpol staff," the detective said.