A man has been charged with the murder of a mother of three in Greymouth.

Police confirmed a 45-year-old-man had been charged after Hayley Williams was shot on Sunday.

He is scheduled to appear in Greymouth District Court this morning.

George Sean Warren, 45, was arrested near Arahura Marae yesterday in a small township about 33km south of Greymouth.

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Police had earlier issued an alert for the man, who was wanted in connection with shooting Williams, 43, at her home in Greymouth on Sunday afternoon.

West Coast area commander Inspector Mel Aitken said Warren had been found walking on the Old Christchurch Rd near the marae.

Several West Coast armed police and CIB members arrested Warren, who gave himself up, Aitken said.

"It was a very peaceful resolution," Aitken said.

"Phenomenal" help from locals in the past 24 hours had helped police track down Warren.

Police are no longer seeking anyone else in relation to the shooting, she said yesterday.

It's understood that Williams, 43, had three children. Police believe Williams and the shooter may have known each other.

Amanda Williams, a friend of Hayley Williams, described her as a "very kind and compassionate lady".

"No way did she ever deserve that," she wrote on Facebook.

"I'm broken ... gutted... sick to my stomach."

Police confirmed "a number" of children were at the property when the shooting happened but declined to comment on whether any were related to Williams.

Police were confident there was no further threat to public safety.

Aitken said people living near the shooting on Marsden Rd should expect to continue to see investigators over the next week.

"West Coast Police are grateful to the public for helping us," she said.

"With the assistance of the public and the commitment of our staff, police were able to make an arrest within 24 hours."