Australians will have a government that makes them proud and Labor will immediately begin working to implement its agenda, Prime Minister Anthony Albanese says. 

Counting from Saturday’s election is yet to confirm whether he will govern in a majority, but Mr Albanese remains confident Labor will secure the required 76 seats. 

But crossbench MPs Rebekha Sharkie, Bob Katter, Zali Steggall, Andrew Wilkie and Helen Haines had already confirmed they would not support a vote of no confidence against the new government, he said. 

“It is important that we respect the outcome of the election on Saturday … I will treat (crossbenchers) with respect,” he told reporters in Canberra on Monday. 

Mr Albanese was accompanied by incoming Deputy Prime Minister Richard Marles, Foreign Minister Penny Wong, Treasurer Jim Chalmers and Finance Minister Katy Gallagher following a swearing-in ceremony at Government House. 

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 travelling to Tokyo on Monday afternoon 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. 

“I will try to run a family-friendly parliament,” he said, noting school holidays were scheduled for July.

The head of the Department of Prime Minister and Cabinet Phil Gaetjens has been temporarily replaced by the deputy secretary Stephanie Foster.

On Monday morning, official figures from the Australian Electoral Commission had Labor on 75 seats in the House of Representatives – one short of a majority – but the party is projected to hold as many as 77.

The Liberal-National coalition had 58 seats and Scott Morrison is 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.

The AEC has listed six seats where the two-candidate preferred vote is so far unavailable: Griffith, Macnamara, Maranoa, Melbourne, Richmond and Sydney.

Three are formally listed as “close”: Sturt, Gilmore and Menzies.

Incumbent MPs are trailing in 20 seats: Swan, Pearce, Tangney, Hasluck, Curtin (WA); Chisholm, Higgins, Kooyong, Goldstein, Deakin (Victoria); Gilmore, Wentworth, Reid, North Sydney, Robertson, Mackellar, Fowler, Bennelong (NSW); Boothby and Grey (SA).

The final result has been projected as 77 for Labor, 59 for the coalition and 15 on the crossbench.

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.” 

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.

By Maeve Bannister in Canberra