Julia Gillard became Australia's first female prime minister on Thursday, as Kevin Rudd made an emotional and ignominious exit, saying she would call an election in coming months and asking voters to trust her.

Gillard immediately offered to end a bitter dispute over a controversial "super profits" resources tax, which is threatening $20 billion worth of investment and has rattled voters, saying she would throw open the door for fresh negotiations.

"I asked my colleagues to make a leadership change because I believed that a good government was losing its way," said Gillard.

The Australian dollar briefly jumped after the leadership change, while shares in BHP Billiton, the world's biggest miner, and Rio Tinto rose around 2 percent, on hopes of a mining tax compromise.   

Centrebet bookmaker on Thursday made Labor outright favourite to win the next election, expected around October, after Rudd stepped down in favour of Gillard.

Gillard's takeover would see the government's resurrect its failed climate change policy, a carbon trade emissions scheme, with Gillard saying she was disappointed in the government's failure to pass laws to set a price on carbon.

"If elected as prime minister I will re-prosecute the case for a carbon price at home and abroad. I will do that as global economic conditions improve and our economy continues to strengthen."    

Rudd become the shortest-serving Australian prime minister since 1972, with his leadership falling apart after a string of poor opinion polls showed him losing ground over recent decisions to shelve a carbon-reduction scheme and impose a new mining tax.

"I have given my absolute all. I was elected by the Australian people as the prime minister...to bring back a fair go for all Australians," said Rudd, choking bad tears.

Government lawmakers believe Gillard has a better chance of winning back voters ahead of elections because she is a warmer personality who can sell policies more effectively.   

Gillard is expected to quickly establish her differences with the Rudd administration by pledging a more consultative leadership, and action to resolve such vote-shredding issues as the stalemate over the Resource Super Profit Tax.

Gillard will automatically attract a large female vote, especially when compared with conservative opposition leader Tony Abbott, who is anti-abortion and opposes sex before mariage.

A recent opinion poll showed, female voters would ditch Abbott for Gillard, favouring the female leader by a commanding 53 percent to 23 percent for Abbott. - Reuters