Australians will have a government that makes them proud and Labor will immediately begin working to implement its agenda, Prime Minister Anthony Albanese says.
The latest official figures from Saturday's federal election have Labor on track to hold 76 seats, allowing Mr Albanese to govern without the support of independents.
But with counting continuing, on Monday evening there were six seats with margins under 1000 votes and six seats where the electoral commission has not published a two-candidate preferred result.
Having been sworn in at Government House on Monday ahead of a trip to Tokyo, Mr Albanese confirmed crossbenchers Rebekha Sharkie, Bob Katter, Zali Steggall, Andrew Wilkie and Helen Haines had stated they would not support a no confidence motion in parliament.
"It is important that we respect the outcome of the election on Saturday ... I will treat (crossbenchers) with respect," Mr Albanese told reporters in Canberra.
Also sworn in were Deputy Prime Minister Richard Marles, Foreign Minister Penny Wong, Treasurer Jim Chalmers and Finance Minister Katy Gallagher.
The ministers will cover all portfolios until the Labor caucus can meet next Tuesday to establish a full ministry.
Mr Albanese and Senator Wong are due into Tokyo on Monday evening for the Quad meeting with leaders of the United States, Japan and India.
The prime minister and foreign minister will return to Australia on Wednesday.
Senior Labor ministers are already working to fulfil the government's election promises.
"I look forward to leading a government that makes Australians proud," Mr Albanese said.
"A government that doesn't seek to divide, that doesn't seek to have wedges, but seeks to bring people together for our common interest and our common purpose."
The prime minister expects the first sitting week of the 47th parliament to be held by the end of July.
The head of the Department of Prime Minister and Cabinet Phil Gaetjens has been temporarily replaced by the deputy secretary Stephanie Foster.
The Liberal-National coalition had 58 seats in the latest count, with Scott Morrison set to stand down from the Liberal Party leadership once a party room meeting can be scheduled.
He is widely expected to be replaced by outgoing defence minister Peter Dutton, who may face resistance from moderates in the party.
Former communications minister Paul Fletcher said he was confident the party would find a "strong leader", but would not comment on leadership candidates.
Party colleague James Paterson said a consensus was forming around Mr Dutton as leader.
Outgoing deputy prime minister Barnaby Joyce said his future as Nationals leader was in the hands of his party room colleagues.
Mr Joyce said the fact that his party held all its seats and picked up a senator showed its "game plan" was working.
"We reflect on the fact that we won every seat that we held (and) three of those were seats ... had retiring members," he said.
The Greens, having secured a record primary vote, are on track to hold 12 Senate seats in the new parliament and up to five lower house seats.
The Senate result remains undetermined, but the coalition is on track to hold 30 seats and Labor 25 in the 76-seat chamber from July 1.
