Incoming prime minister Anthony Albanese is still days away from knowing whether he can govern with a majority.

But the Labor leader will be sworn in on Monday, along with his deputy Richard Marles, new Treasurer Jim Chalmers and new Finance Minister Katy Gallagher.

Reflecting on Labor’s election win on Sunday morning in Sydney, Mr Albanese said it had been a “big moment”.

“But what I want it to be is a big moment for the country.”

Official figures from the Australian Electoral Commission have Labor on 74 seats in the House of Representatives – two short of a majority – but the party is projected to hold as many as 77.

The Liberal-National coalition held 52 seats, with Scott Morrison set to stand down from the Liberal Party leadership once a party room meeting can be scheduled.

An emotional Mr Morrison told his local Horizon Church on Sunday a life of faith called on people to “trust and obey”.

“God holds us, whether you’re a prime minister or a pastor, running a business, teaching in schools, working in the police force – it doesn’t matter,” he said.

“I’m very pleased that the last thing I say as PM is here.”

He is widely expected to be replaced by outgoing defence minister Peter Dutton, but Mr Dutton may face resistance from moderates in the party.

Mr Albanese and Senator Wong will travel to Tokyo on Monday for the Quad meeting with the leaders of the US, India and Japan, as well as bilateral meetings.

He will return to Australia on Wednesday when he plans to “get down to business”.

One of the first major events will be a meeting with state premiers and territory chief ministers when he will set out the new federal government’s stance on more ambitious climate action.

Ten independents are on track for victory and will be joined on the crossbench by sitting Mayo MP Rebekha Sharkie from the Centre Alliance and veteran Kennedy MP Bob Katter.

The AEC has listed 13 seats where the two-candidate preferred vote is so far unavailable: Bradfield, Calare, Canberra, Cowper, Grey, Griffith, Hinkler, Macnamara, Maranoa, Melbourne, Richmond, Ryan and Sydney.

Four seats are formally listed as “close”: Sturt (SA), Gilmore (NSW), Menzies (Victoria) and Moore (WA).

Incumbent MPs are trailing in 18 seats: Swan, Pearce, Tangney, Hasluck, Curtin (WA); Chisholm, Higgins, Kooyong, Goldstein, Deakin (Victoria); Wentworth, Reid, North Sydney, Robertson, Mackellar, Fowler and Bennelong (NSW); and Boothby (SA).

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

Liberal frontbencher Jane Hume said the best result would be a majority parliament.

“A hung parliament is dysfunctional and won’t serve the country well,” she told Sky News on Sunday.

Outgoing deputy prime minister Barnaby Joyce said his future as Nationals leader was in the hands of his party room colleagues.

Independent candidates elected on Saturday will be pushing the government to deliver on three issues: a more ambitious climate policy, a national integrity commission and women’s equality.

Monique Ryan, who is on track to seize the seat of Kooyong from outgoing Treasurer Josh Frydenberg, said voters had responded to a coalition government shifting “too far to the right”.

“It has been dragged to the right by the Nationals … and it is no longer representing the small ‘l’ Liberal heartland,” Dr Ryan said.

Moderate Liberal and outgoing minister Simon Birmingham said the party needed to step up its 2030 emissions target and do more to preselect women in safe seats.

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 greenslide is set to grow in the coming days – people have delivered a mandate for action on climate and inequality,” leader Adam Bandt said.

The final result of the half-Senate election is yet to be determined, but it is expected veteran One Nation leader Pauline Hanson will not be returned in Queensland.

And for the first time in the ACT’s history, it is expected the Liberals will not pick up a Senate seat with independent candidate and former Wallaby David Pocock tipped to defeat outgoing minister Zed Seselja on preferences.

By Paul Osborne in Canberra