Christine Assange accused Gillard of being out of step with global opinion over her son's work and warned she would face the wrath of voters if he did not apologise.
"I really do think she (Gillard) could lose an election over this," Christine Assange was reported by The Australian Saturday as saying in a statement.
"It is a sign of a mature person to stand up and say: 'Okay I was wrong, I apologise, I was wrong about this person'. That's what she should be doing."
The mother added: "It would appear the prime minister is not only uninformed about one of her own highly honoured citizens but completely out of step with prevailing world opinion."
Assange accused the prime minister of labelling her son a "criminal" and of defaming him in public.
The statement comes at a time when the WikiLeaks founder prepares to face a court in London to determine whether or not he will be extradited to Sweden to face sex-related allegations.
Gillard has labelled the release of documents by WikiLeaks as "illegal" and "grossly irresponsible".
An Australian Federal Police investigation found WikiLeaks had broken no domestic law.Julian Assange remains in good spirits, his mother said. "He's bearing up well, considering.
"It's tying up his time and his money and it's taking a focus away from what he's trying to achieve regarding his work.
"I think that is what he's finding frustrating, the fact it's diverting attention to petty things."
Julian Assange made a public appeal Friday night to Gillard to help bring him back to Australia from the UK, the ABC reported Saturday.
"Julia Gillard should be taking active steps to bring me home and to protect our people," he told a public forum in Melbourne in a pre-recorded speech.
"She should be contacting the US embassy and demanding that it back off."
Assange this week became only the third person in 14 years to be awarded the Sydney Peace Foundation's gold medal - an award previously given only to the Dalai Lama,
Nelson Mandela and Japanese Buddhist leader Daisaku Ikeda.
The Sydney award was announced on the same day it was confirmed that Assange had been nominated for the Nobel Peace Prize.
He has been the recipient of several high-profile international awards, including Le Monde's Person of the Year 2010.