In his first press conference in Canberra since his landslide election win, the prime minister said he was confident of setting up Australia for decades to come.
"Today, we continue the work of continuing to build Australia's future," he told reporters on Monday.
"I said before the last election that you needed more than one term as a Labor government, and I sought that from the first day ... I became Labor leader back in 2019.
"I want Labor to be the natural party of government."
The prime minister confirmed he had spoken to multiple world leaders since Saturday's win, including US President Donald Trump.
He confirmed his first overseas trip would be to Indonesia and that he had accepted an invitation from Canada's new prime minister Mark Carney to attend the G7 summit in June.
With an increased majority in parliament, Mr Albanese said he had a large agenda but was not looking to get ahead of himself.
"We're not getting carried away. We've been an orderly government. We've been a reform government," he said.
"We'll continue to be an ambitious government ... and we'll continue to engage."
Mr Albanese and his leadership team will meet on Monday to decide a timeline for naming a new ministry and a caucus meeting, which will showcase a swathe of new faces in the party room.
Depending on the final vote count, the delicate factional balance in the ministry could stir a wider reshuffle, under an ascendant left wing.
Labor, under Mr Albanese, picked up more than a dozen seats, with more on the table as ballot counting continues. The government needed at least 76 out of 150 lower house seats to win and could end up with 85 or more.
The government faces a weakened opposition, with the battered Liberals losing at least 13 seats, and potentially as many as 19, and is sitting on 39 so far.
Leader Peter Dutton was the highest-profile casualty, becoming the first opposition leader to lose his seat as three Liberal frontbenchers were booted from parliament by Labor candidates.
After Mr Dutton's loss in Dickson, the leadership frontrunners include shadow treasurer Angus Taylor, deputy Liberal leader Sussan Ley, defence spokesman Andrew Hastie and immigration spokesman Dan Tehan.
On Monday, some of the Liberal party's senators conceded the coalition had failed to offer voters a substantial policy platform, especially on the economy.
"You've got to have the ambition to lead on the economy and ... I don't think that's been evident over the last few years," Liberal senator Andrew Bragg told ABC radio.
The coalition needed to avoid culture wars that targeted minorities and become more inclusive to win back the middle ground, he said, while branding a decision to preference One Nation as "misguided".
Senate colleague Hollie Hughes, who lost her party's pre-selection, was scathing of Mr Taylor's role in the defeat saying "the economic narrative was just completely non-existent" and there were questions about his capability.
Treasurer Jim Chalmers joined the pile-on, saying it would be "extraordinary if Angus Taylor was rewarded with a promotion after the diabolical contribution that he made to this history-making coalition defeat".
The nosedive in the Liberal vote has also cost the Greens seats, after support for Labor surged and Liberal preferences flowed to the government rather than the minor party.
It cost them Griffith in Brisbane while leader Adam Bandt is fighting to retain his seat of Melbourne, although there's confidence he will prevail. Other Greens seats remain in doubt.
But Mr Bandt remains defiant, saying the party's vote had hit a record high and that it would use its balance of power in the Senate to push for progressive reforms.
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