Invercargill shooting victim Verity McLean will be farewelled at a private funeral service next week.

The 40-year-old was allegedly murdered by her husband Ben McLean, a local police officer.

He has also been charged with the attempted murder of Garry Duggan who his wife was believed to be in a relationship with.

Police say McLean's funeral will be a private event but her family are considering holding a public memorial service.

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Southern District Commander Superintendent Paul Basham says police have been particularly touched this week by the reaction of the community:

"I would like to express my deep appreciation for the support shown to Invercargill police both from the local community and beyond. This means so much to our staff. We are acutely aware of the impact an event like this has across the community, of which we are a part. It is at times like this that our community really shows its strength.

"Our focus in the coming days will be to continue supporting all the families impacted by this tragedy, ensuring a meticulous, impartial investigation continues, and supporting our own staff who have been affected." said Basham.

The investigation into the shooting, which includes ongoing scene examinations, forensic analysis and witness interviews, will continue into the weekend.

Garry Duggan remains in Southland Hospital in a stable condition.