"The community can be assured that there is no information to suggest a current of impending threat related to these search warrant," police said in a statement.
Tarrant's mother and sister have been moved to a safe house by police.
His father, Rodney Tarrant, in 2010 died at the age of 49, from lung cancer.
"We're all gobsmacked, we don't know what to think," Tarrant's 81-year-old grandmother Marie Fitzgerald, told Australia's 9News in an interview.
"The media said he's planned for a long time, so he's obviously not of sound mind, I don't think."
Tarrant's uncle, Terry Fitzgerald, apologised to the families of the dead and injured in New Zealand. "We can't think nothing else, just want to go home and hide," he told 9News.