With counting from Saturday’s election yet to confirm whether he will govern in majority, Albanese on Monday attended Government House in Canberra with incoming 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 the week after next to put in place a full ministry.

Albanese and Wong will head to Tokyo on Monday afternoon for the Quad meeting with Biden, host leader Fumio Kishida and Indian prime minister Narendra Modi.

The prime minister issued a statement on Sunday night, saying he would use the meeting to talk about his government’s ambitions to tackle climate change and pursue a stronger foreign policy focus on the region.

“This will be my first international trip as prime minister and I am honoured to represent Australia at this important forum,” the statement read.

“The Quad Leaders’ Summit brings together four leaders of great liberal democracies – Australia, Japan, India, and the United States of America – in support of a free, open and resilient Indo-Pacific, with the Association of Southeast Asian Nations (ASEAN) at its centre.

“Under my government, Australia will continue to work through the Quad to deliver positive and practical initiatives in our region, including on health, security, and climate change.”

Biden spoke with Mr Albanese on Sunday and reaffirmed US commitment to the US-Australia alliance.

“President Biden expressed deep appreciation for the Prime Minister-designate’s own early commitment to the alliance, reflected in his decision to travel almost immediately to Tokyo to attend the Quad Summit,” a US government readout of the call said.

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.

Speaking before her swearing in, Gallagher was quietly confident Labor woukd reach a majority.

“We’re hopeful for a majority government but there’s more votes to be counted. That’s the reality. We’ve got a few more days to go,” she told ABC News Breakfast on Monday.

“There’s certainly a strong and credible path to a majority for us.”

A swathe of incoming independents are expected to make a crossbench of at least 15 members.

Regardless of the make up of parliament, Albanese would work with the crossbench to bring the country together, Gallagher said.

“We’re going to have a bigger crossbench without a doubt and Anthony is exactly the type of prime minister who has the skills and strength to deal with that,” she told ABC Radio National.

“The people of Australia voted for change on the weekend, not just in terms of government, they voted in terms of change about how they want to see the parliament work and Anthony’s just the right guy for the job to deal with that.”

Less than 48 hours after the federal election, work had already started to audit the existing budget and find instances of waste, Treasurer Jim Chalmers said.

He expects to deliver Labor’s first budget in nine years at the end of October.

“This is probably the trickiest set of economic conditions that a new government and new treasurer has inherited,” he told Sky News.

Two thirds of voters supported a minor party with their first preference, and senior Labor figure Tanya Plibersek said the incoming government would learn from the recent campaign to address voter dissatisfaction.

Plibersek, expected to take on the education portfolio, told the Seven Network that once the dust had settled after the election Labor needed to have a close look at why people were turning away from the major parties.