DAR ES SALAAM (AFP) - US President Barack Obama on Monday called both reinstalled Australian Prime Minister Kevin Rudd and the woman he ousted Julia Gillard, two bitter rivals with whom he has friendly relations.

Mr Obama called the dueling Australians from Air Force One as he flew from Cape Town to Tanzania, the final leg of his Africa tour.

"In his call with Prime Minister Rudd, the President congratulated the Prime Minister on his return to office," the White House said in a statement.

"The President also reiterated the enduring strength of the US-Australia alliance and his confidence that the United States and Australia will continue to work together closely on important global and regional issues.

Mr Rudd and Mr Obama also discussed the proposed Trans-Pacific Partnership trade deal.

"In his call with former Prime Minister Gillard, President Obama thanked her for her warm friendship and close partnership in deepening cooperation between the United States and Australia, and he wished her well in her future endeavors."

Mr Rudd was sworn in as Australia's new prime minister on Thursday almost three years to the day since he was ousted from the job by Gillard, as their Labor Party desperately fights for electoral survival.

The 55-year-old sealed his dramatic return after a leadership ballot on Wednesday, in which Ms Gillard, the country's first female premier, was deposed in a party-room vote and announced her retirement from politics.