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Malcolm Turnbull has been sworn in as Australia’s new prime minister, after Tony Abbott was ousted by his party in a leadership challenge.

Mr Abbott on Tuesday said his removal was “tough” but pledged to “make this change as easy as I can”.

As he prepared to take office, Mr Turnbull said it was “the most exciting time to be an Australian”.

Mr Turnbull, communications minister under Mr Abbott, is Australia’s fourth prime minister since 2013.

“I’m filled with optimism and we will be setting out in the weeks ahead and the months ahead more of those foundations that will ensure our prosperity in the years ahead,” he told journalists.

He is expected to preside over a meeting of Liberal MPs on Tuesday morning and then hold a meeting of the joint Liberal-National coalition parties.

Out going leader

Mr Abbott finally spoke publicly on Tuesday morning, saying his government was not perfect but listing his achievements.

He did not say if he would remain on the backbench or eventually resign from politics.

“It is a tough day but when you join the game you accept the rules,” he told journalists, while also taking swipes at party members who had leaked to the media and carried out anonymous character assassinations.

Mr Turnbull is not expected to announce a new cabinet line-up until the end of the week.

But there was speculation even before the ballot that Joe Hockey might lose the Treasury portfolio.

Political pundits have suggested Social Services Minister Scott Morrison might become the new treasurer.

Deputy Liberal Party leader Julie Bishop, who on Monday threw her support behind Mr Turnbull, said that earlier in the year after surviving his first challenge, Mr Abbott had asked for six months to turn the Liberal Party’s electoral hopes around.

“Tony had done a fantastic job in winning the 2013 election and there was so much hope and so much expectation, but last February, a number of people felt that he hadn’t met their expectations,” she told journalists.

“He asked for six months, and the party gave him that six months, and now seven months later the majority have decided they wanted a change of leader and that he had lost their confidence.”

Ms Bishop, who is foreign affairs minister and was re-elected as deputy leader on Monday, said it was a difficult time for Mr Abbott.

“He was calm, he was obviously very hurt,” she said.

Mr Turnbull said on Monday night the government would serve a full term, meaning a general election is likely in mid-2016.

The first real test of how the public has taken the news will be on Saturday in a by-election for the seat of Canning in Western Australia.

The seat is held by the Liberal Party. Opinion polling done before Monday night’s ballot suggested the Liberals would retain the seat but at a reduced majority. (BBC)