The prime minister said while his own views on Australia becoming a republic were well known, it was not the time to have discussions on changing the country's system of government.
"Now is a time for us to pay tribute to the life of Queen Elizabeth, a life well lived of dedication and loyalty including to the Australian people," he told the ABC's Insiders program.
"Quite clearly, this is a time of national mourning."
The prime minister will recommend Governor-General David Hurley issue the Australian proclamation of King Charles III's accession to the throne during a meeting of the Executive Council at Government House.
It will then be followed by a proclamation ceremony at Parliament House at midday on Sunday.
Ahead of the proclamation, the prime minister said the new king represented a new era for the country.
King Charles III has been outspoken on issues such as climate change during his time as prince, and Mr Albanese said it would still be appropriate for him to do so as monarch.
"I think that dealing with the challenge of climate change shouldn't be seen as a political issue, it should be seen as an issue that is about humanity and about our very quality of life," he said.
"King Charles has identified that for a long period of time, and I think engagement in issues is very different from engagement in party political matters.
"King Charles of course represents a new era. The second Elizabethan era has now passed, King Charles will need to forge his own path."
The prime minister said he also respected the views of Indigenous Australians, with some seeing the late Queen as a representation of colonialism and dispossession of land.
"As Prime Minister, I'm not in a position to control people's feelings," he said.
"Many of those will of course be heartfelt, but this loss is, I think, for us to come together at this time as a nation."
Opposition Leader Peter Dutton said the new king would have picked up many of the traits Queen Elizabeth had displayed during her 70-year reign.
"That will be a good thing for the United Kingdom and, frankly, for the Commonwealth," he told ABC's Insiders program.
"We need the King as much as we did a Queen because we have a stability in our system that ha served us well, and I don't believe in disrupting that."
Former prime minister John Howard remembered the late Queen Elizabeth II as the most accomplished leader he dealt with during his long political career.
Mr Howard, who met with the Queen on 25 occasions paid tribute to the monarch's sense of duty.
"(She was) a great leader, an impeccable constitutional monarch, somebody who had enormous affection for our country," he told Sky News on Sunday.
"Whenever I saw her, she was across the recent political developments in Australia ... she would ask about them but not in a way that represented any kind of interference," Mr Howard said.
"She was very familiar with things that we had done and things we'd achieved and the challenges the country had."
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