Numbers tallied by the Australian Electoral Commission show Labor currently leading with 76 seats. But some, including the seat of Gilmore on the NSW south coast, are too close to call.
On Monday morning senior Labor figures were not ready to claim a majority government victory, but said there was a "strong and credible path" towards it.
"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," newly sworn in Finance Minister Katy Gallagher told ABC News Breakfast on Monday.
The latest Australian Electoral Commission figures have Labor ahead in 76 seats and the coalition with 58 MPs.
Postal votes will continue to be received and counted until June 3 and the writs will be returned on or before June 28.
Prime Minister Anthony Albanese, Deputy Prime Minister Richard Marles, Foreign Minister Penny Wong, Treasurer Jim Chalmers and Finance Minister Katy Gallagher were sworn in by Governor-General David Hurley in Canberra on Monday.
Mr Albanese is travelling to Tokyo with Senator Wong for a summit with leaders of the US, Japan and India.
But the seat count continues as a swathe of incoming independents are expected to comprise a large cross bench of at least 15 members.
Prior to the election there were seven crossbenchers.
Regardless of the parliamentary make up, the prime minister will work with the cross bench to bring the country together, Senator 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 has already started to audit the existing budget and find instances of waste, Treasurer Jim Chalmers says.
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.
A third 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 such dissatisfaction.
Ms Plibersek, expected to take on the education portfolio, told the Seven Network that Labor needed to have a close look at why people were turning away from the major parties.
Labor is expected to finalise its ministry next Tuesday once the caucus meets.
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