Australia's new prime minister Malcolm Turnbull has indicated he is in no hurry to sever the nation's constitutional links to Britain by appointing an Australian president as head of state.

Mr Turnbull led the Australian Republican Movement, an advocacy group, when it failed at a 1999 referendum to convince Australians to replace the Queen as Australia's head of state.

But six days after becoming prime minister, Mr Turnbull said he had no plans to revisit the divisive constitutional issue.

"While I am a republican, I have to say to you that there are much more immediate issues facing me and the government than the republic, and the key ones all relate to economic growth," Mr Turnbull said

Governor General Peter Cosgrove, the Queen's representative in Australia, has sworn in Mr Turnbull's first 21-member cabinet.

Mr Turnbull has announced a younger team of ministers that included more women than the 19-member cabinet of his predecessor, Tony Abbott.

"Today we are forming a government for the 21st century, a ministry whose composition and focus reflect our determination to ensure that Australia seizes the opportunities of these, the most exciting times in human history," Mr Turnbull told the swearing in ceremony.

Mr Abbott was defeated in a surprise leadership ballot of MPs within the ruling Liberal Party last week after he fought poor opinion polling during most of his centre-right government's two years in power.

Mr Abbott is a staunch monarchist who angered many conservatives by making the Duke of Edinburgh an Australian knight on Australia's national day on January 26.