Police investigate the scene where a man suspected of a double homicide was fatally shot by police after a car chase around Tauranga city.

A woman's body has been found by police investigating this week's double homicide in Tauranga.

The body was found on Friday when police were called to a Tauranga home, District Commander Superintendent Andy McGregor said in a statement on Saturday.

GOOGLE MAPS The body was found on Friday when police were called to a Lynwood Place address in Tauranga.

Police believed the woman had been dead for a couple of days and was likely the victim of a domestic incident. They were not seeking anyone else in relation to the death.

McGregor also commented Saturday on the double homicide investigation, saying police were making good progress and had established that the incident appeared unrelated to gang conflict, despite it involving gang members.

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McGregor said the woman's sudden death at the Lynwood Place address in Tauranga appeared to be linked to the double homicide.

The woman was the fourth death in a traumatic week for Tauranga. Following the double homicide in outer suburb Omanawa on Tuesday, police were involved in a dramatic shootout with a gang member who they killed on Thursday night.

Police fatally wounded the gunman after several exchanges of gunfire, including from a moving vehicle. The shootout began when police attempted to stop a car which they were interested in as part of their double homicide investigation.

Shots were fired on them and the vehicle fled. There was gunfire from the moving vehicle before it eventually pulled over near Tauranga's CBD and an occupant got out and began firing on the chasing police. This man was killed in the ensuing exchange.

DOMINICO ZAPATA/STUFF Police investigate the scene where a man suspected of a double homicide was fatally shot by police after a car chase around Tauranga city.

McGregor said the driver fired about 15-20 shots. Police believed it was a semi-automatic weapon due to the number of shots fired in quick succession.

Detective Inspector Mark Loper said on Thursday they were "still working to understand the circumstances of the deaths and the involvement of any other parties".

"While police have spoken to a number of people in relation to the incident, we believe there may be others who are yet to talk to us."

CHRISTEL YARDLEY/STUFF Police guard the scene on Ormsby Rd after two people were shot and killed.

On Friday, the investigation reached down into Christchurch where an armed police operation was undertaken and a 25-year-old Auckland man was arrested.

He was later charged with the murders of the two men found dead in Omanawa and made a first appearance in court on Saturday morning.

The heavily tattooed 25-year-old appeared in the Christchurch District Court before Judge Tony Couch, facing two charges of murder for the two victims who police have said were known to each other.

His lawyer, Moana Cole, sought an interim name suppression order for him claiming it was a "high-profile case" and said there was a risk of retaliation. Judge Couch granted the interim suppression order.

Police also sought an interim order suppressing the names of both victims and the summary of facts, which was also granted by Judge Couch.

The 25-year-old was remanded in custody to appear in the Tauranga District Court on February 26.