Anthony Albanese and four senior frontbenchers sworn in ahead of Quad trip

Anthony Albanese has been sworn in as Australia's 31st prime minister, as his incoming Labor government takes power after almost a decade of Coalition rule.

Mr Albanese gave his first press conference as Prime Minister soon after being sworn in, flanked by several of his new ministers and a symbolic first change behind him. The incoming government has added the Aboriginal and Torres Strait Islander flags alongside the Australian flag.

The weekend's election result has the Liberal Party on the hunt for a new leader, with Peter Dutton emerging as the most likely replacement for Scott Morrison.

Mr Albanese was sworn in with his deputy, Richard Marles, and frontbenchers Penny Wong, Jim Chalmers and Katy Gallagher.

Mr Marles was sworn in as Employment Minister, Senator Wong as Foreign Affairs Minister, Mr Chalmers as Treasurer and Senator Gallagher as Finance Minister, Minister for Women and Attorney-General.

The Prime Minister and Senator Wong have flown to Japan on Monday to meet with the leaders of the Quad — the United States, India and Japan.

"Travelling to the Quad meeting in week one signifies how important we believe this partnership is for our security," Senator Wong said in a statement. 

“And we will be taking new energy and much more to the table — including our commitment to act on climate change after a lost decade."

US President Joe Biden phoned Mr Albanese late on Sunday, congratulating him on the win and thanking him for choosing to travel to Tokyo for the meeting.

There has been uncertainty about what role Mr Marles will hold. As deputy leader, he can pick his portfolio and there is speculation he wants to return to defence. Clarity on this will come next week when the full frontbench is sworn in.

Mr Albanese wants national cabinet to meet in person in the coming weeks as he sets about implementing his agenda. 

He said the new parliament would sit for the first time before the end of July, but that he was still seeking advice from the Department of Prime Minister and Cabinet about when would be the most reasonable time for it to return.

Dutton emerging as next Liberal leader

Liberal sources have told the ABC that Mr Dutton, who served as a senior cabinet minister throughout the Coalition's three terms, has emerged as the frontrunner to replace Mr Morrison. 

Treasurer Josh Frydenberg was among the biggest victims of the Coalition's loss, losing both his seat and the likely leadership of the Liberals in opposition.

The ABC has been told by sources that, without Mr Frydenberg, Mr Dutton appeared to have the numbers to become leader.

Sources have also told the ABC that South Australian senator Anne Ruston is being touted as a possible deputy to Mr Dutton, with Liberals conceding they need to do more to get women into their ranks.

About half the Liberal women in the lower house lost their seats in this election, fuelling the need for a woman to play a senior role in the leadership.

Cabinet ministers Karen Andrews and Sussan Ley's names have also been touted, but their support in the party room remains unclear.

Bridget Archer, who retained her seat — despite it being the Coalition's most marginal — told the ABC on Monday morning that she was considering nominating to be deputy leader, vowing to be a vocal, moderate voice.

The Liberal Party's greatest losses came thanks to teal independents — women who wiped out moderate Liberals from once-safe seats in Sydney, Melbourne and Perth.

Liberal sources expect Mr Frydenberg will mount a political comeback but his path back to the parliament remains unclear.

"I still have fire in my belly," he said on Sunday morning, while refusing to concede until postal votes were counted.

New parliament brings mixed Labor fortunes

Labor has lost two women from its cabinet ranks, with Kristina Keneally's attempt to be parachuted into a safe Western Sydney seat failing, and Terri Butler losing her Brisbane seat to the Greens.

The Greens will enter the next parliament with record numbers in their ranks. The party will hit a high-water mark of 12 in the Senate, where it now holds the balance of power.

Thanks to gains in Queensland, the party has also added to its lower house seats.

Labor had a big night in Perth, wiping out Coalition cabinet ministers and once-safe, prized Liberal seats.

Attorney-General Michaelia Cash, the deputy Liberal leader in the Senate, blamed Mr Morrison for the party's fortunes in the west.

She said his decision to initially back Clive Palmer's legal action against WA's closed border proved costly, with Mr Morrison's close confidant Ben Morton losing his Perth seat.

"We — Senator Cash and Mr Morton — did not support siding with Clive Palmer but the decision was made that we would," she said.

How can he become Prime Minister without majority?

As of Monday morning, Labor was yet to reach the 76 seats needed to form government.

If it falls short, it will need the support of the crossbench to pass legislation in the House of Representatives.

To be sworn in as Prime Minister, Governor-General David Hurley needed to be convinced that Mr Albanese would be able to govern in some form.

The election results have shown that Labor was the only major party that would be able to govern — either in majority or minority.

If the results had been closer and it was clear there would be a hung parliament, but no clarity around which party would secure the support of the crossbench to form government, then the Governor-General would not have agreed to swear in Mr Albanese or Scott Morrison.

The Governor-General has to have confidence that whoever becomes prime minister will be able to maintain a stable government, whether that's with the support of the crossbench or not.

He also would have received legal advice before the swearing-in to make sure it was the right decision.

Usually there would not be the kind of rush there is this time around, but the Quad leaders meeting in Tokyo has meant the process has had to be expedited.

Crossbench keen to flex its muscle

Mr Albanese said he had already received assurances from several independents that they would support his government if Labor was unable to secure a majority in its own right.

"I have received and have had discussions with the existing members of the crossbench and received confirmation from Rebekha Sharkie, Bob Katter, Andrew Wilkie, Helen Haines and Zali Steggall that they would not support any no-confidence motions against the government, and that they would also secure supply," Mr Albanese said.

Incoming teal independents Monique Ryan, who defeated Mr Frydenberg, Zoe Daniel, who defeated Tim Wilson, and Allegra Spender, who defeated Dave Sharma, have said they want the incoming government to take greater steps to address climate change.

In the Senate, if it is unable to reach an agreement with the Coalition, it will need the Greens and, likely, Jacqui Lambie to pass legislation.