Australia's new Prime Minister Malcom Turnbull indicated on Monday that he is in no hurry to sever the nation's constitutional links to Britain by appointing an Australian president as head of state.

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

But six days after becoming prime minister, 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," Turnbull told Nine Network television.

Governor General Peter Gosgrove, the British monarch's representative in Australia, swore in Turnbull's first 21-member Cabinet later on Monday.

Turnbull on Sunday 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 21at 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," Turnbull told the swearing in ceremony Monday.

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

Abbott is a staunch monarchist who riled many conservatives by making the Queen's husband, Prince Philip, an Australian knight on Australia's national day on Jan. 26. Many thought an Australian citizen would have been a more appropriate choice for the honour.

Many believe that with both the prime minister and opposition leader Bill Shorten now supporting an Australian republic, the constitutional change could now be possible. Opinion polls suggest that most Australians believe that they should have an Australian head of state.

But Turnbull said there needed to be a "genuine popular movement" for change.

"My own view ... is that the next occasion for the republic referendum to come up is going to be after the end of the Queen's reign," he said. "I think that will be the next watershed event, if you like, to make that issue relevant."

Abbott was not included in the new Cabinet. The government's unpopular chief economics minister, Treasurer Joe Hockey, has been replaced by Social Services Minister Scott Morrison. Hockey has announced he plans to quit politics.

Turnbull would not comment on reports that Hockey will become Australia's next ambassador to the United States.

"I think he's got a lot of national service, as it were, ahead of him in his life," Turnbull said.

The government's popularity crashed in opinion polls and never recovered after Hockey unveiled his first annual budget in May last year. The budget was widely criticized as unfair toward the poor, and a hostile Senate blocked key measures.