Australian TV news networks have shown what they say are the mother and sister of Tarrant returning to their homes in eastern Australia Monday with police searching for clues in the New Zealand mosque attacks.
Australian police said the aim of the search was to obtain material that could help New Zealand police in their investigation of the attack.
New Zealand Police Commissioner Mike Bush said the Australian police searches "haven't discovered any matters that would threaten their public."
The two people identified as mother Sharon Tarrant and sister Lauren Tarrant did not comment to the media after police searched their homes. They are reportedly in protective police custody.
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Separately, a gun shop on Monday acknowledged selling guns to Tarrant online.
At a news conference, Gun City owner David Tipple said the store sold four guns and ammunition to Brenton Harrison Tarrant through a "police-verified online mail order process."
The store "detected nothing extraordinary," about the buyer, he said.
None of the guns sold to Tarrant were military-style, semi-automatic weapons. Ardern has said the attacker used five guns, two of them semi-automatic, which were purchased with an ordinary gun license and modified.
It was not clear if any of the firearms Tarrant purchased from Gun City were used in Friday's shootings.
"My staff and I are dismayed and disgusted by what happened last Friday afternoon," Tipple said. "We cannot comprehend how such despicable actions could be carried out on those at prayer in a place of worship."
Tipple said he felt no responsibility for the tragedy and refused to say whether he believed gun ownership laws should change in New Zealand, insisting a debate over guns should be held at another time.
His store has been criticized for leaving out a roadside advertising billboard that shows a parent helping children with rifle target practice in the wake of the shootings.
"This man wrote in his manifesto that the purpose of using a firearm was to divide us," Tipple said. "If we allow him to make changes in our ideology, in our behavior, he's won."
But New Zealand Prime Minister Jacinda Ardern said on Monday she would announce new gun laws within days.
She said Cabinet ministers had met and made an in-principle decision to tighten gun ownership but details still need to be worked out.
Ardern also announced an inquiry into the country's intelligence services. Tarrant wasn't detected before his well-planned attack on two mosques and there have been concerns intelligence agencies were overly focused on the Muslim community in detecting and preventing security risks.
Meanwhile, relatives of the victims were anxiously waiting for word on when they can bury their loved ones. Islamic tradition calls for bodies to be cleansed and buried as soon as possible after death, usually within 24 hours.
Members of the Muslim community and police were Monday morning at a cemetery which has been fenced off and obscured with white netting. Backhoes had stopped digging and police officers said they were setting up a media area inside the cemetery.
Kawthar Abulaban, 54, who survived the shooting at the Al Noor Mosque, came to the burial site to see the preparations. She did not mind the row of photographers and reporters lined up outside the cemetery.
"It's good for the world to see what's happened because people around the world, they thought we were terrorists because some stupid people, they said they are Muslims, they go and kill innocent people, they thought we are terrorists," said Abulaban who emigrated to New Zealand from Jordan 17 years ago.
"I will not change my opinion about New Zealand. It's my country," she said. "You know I have lots of support, lots of love, lots of kindness from all of the New Zealand people."
Ardern has said authorities hoped to release all the bodies by Wednesday, and Bush said authorities were working with pathologists and coroners to complete the task as soon as they could.