The search for alleged murder victim’s missing remains has again been suspended, after days of intensive searching across a regional seaside town in South Australia.

Julian Story was allegedly murdered last month in the Port Lincoln apartment he shared with his girlfriend, former Beauty And The Geek star Tamika Chesser.

WATCH ABOVE: SAPOL suspends search activity for missing remains of Julian Story.

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South Australian Police allege Chesser, 34, killed and dismembered Story, including cutting off his head, on June 17 — the day after his 39th birthday — before setting his body on fire inside the unit.

Chesser, 34, is charged with murder, disposing of human remains to pervert the course of justice and assaulting a police officer and remains in custody ahead of her next court appearance in December.

Story’s head has not been found.

An earlier weeks-long search for the missing remains — involving detectives, police officers and local SES personnel looking in bushland and along the coastline at Port Lincoln — had been paused until new search locations were identified and investigated earlier this week.

On Thursday, South Australia Police Detective Superintendent Darren Fielke said that latest search will now stop unless police get “specific information”.

On June 27, Story’s family released a statement, thanking the larger South Australian community for their support.

“On behalf of our family, we want to sincerely thank the South Australian Police, emergency services, and first responders for their compassion and professionalism during this devastating time,” they said.

“We are navigating an unimaginable loss, and your care has brought comfort amid the chaos.

“We are also deeply grateful to our family and friends and this extraordinary community, whose kindness and support have helped carry us through.

“Your prayers, presence, and quiet strength mean more than words can say.”

People have appealed for public assistance tracking Chesser’s movements around the time of the alleged murder.

Police released CCTV images of the dark clothing she was seen wearing at the time, including as she walked a dog in the area.

Story will be farewelled in a private funeral on August 6 at St Mary’s of the Angels church in Port Lincoln.