First female prime minister and former leader of the Australian Labour Party Julia Gillard has broken her silence over the party leadership, sexism in politics and losing power to Kevin Rudd.

In a talk with Anne Summers at the Sydney Opera House, Ms Gillard threw a thinly-veiled barb at former prime minister Kevin Rudd for destabilising her government and turning against her despite being in the same party.

Julia Gillard declared the difference of her behaviour and Kevin Rudd's. She said she has always worked for the Labour government to stay in power. Ms Gillard said it was difficult for her to accept her ouster from the party leadership which returned Kevin Rudd back in the seat of power. Ms Gillard thought that the best course of action was to remain silent.

She kept her silence before the election and gave very few public comments. Ms Gillard justified her ouster of Kevin Rudd in 2010 as legitimate when asked to comment on explosive events following Kevin Rudd's return to the post.

Ms Gillard said that it was legitimate to ask the party leader for a leadership vote but to do things that will undermine the Labour government and the party must not be done. Ms Gillard also used her opportunity in the spotlight to deny reports that she and her long-time partner Tim Mathieson had gone their separate ways. She said the rumours were false, referring to a report from Woman's Day.

The Sydney Opera House talk was Ms Gillard's first serious interview after her ouster as prime minister of Australia on June 26.

Ms Gillard also cited the sexism in politics and said she was aware of how she was being treated. She said she chose not to react despite already in a "murderous rage."

Ms Gillard said there was "an underside of sexism, really ugly, violent sexism" in the country. She did not know if it only comes with the new media age and said she would have been depressed if the world has not gotten past that.

Watch a part of Julia Gillard's interview here.