While talks of a republic have been revived following the death of Queen Elizabeth II, Mr Albanese said it was too soon to discuss changing the country's system of government.
He said a referendum to enshrine an Indigenous voice to parliament would be the constitutional priority during his first term.
"I couldn't envisage a circumstance where we changed our head of state to an Australian head of state but still didn't recognise First Nations people in our constitution," he told ABC TV on Monday.
"That's our priorities this term. I made that very clear before the election."
The prime minister said he intended to see parliament resume before the budget is handed down in October.
Federal parliament was due to sit in Canberra this week, but was suspended following the death of Queen Elizabeth II.
Protocol dictates parliament will not sit for 15 days following the death of the Queen.
Key government legislation, such as a bill introducing a federal integrity commission, was set to be introduced to parliament during the sitting week.
Mr Albanese said the days would be made up .
"Tradition, I know, sometimes can be inconvenient, but traditions are important. Traditions and protocols are one of the things that bind us together," he said.
Deputy Prime Minister Richard Marles said the decision to suspend parliament and not debate during the mourning period was sensible.
He said he was confident the government would still be able to pass its signature legislation by the end of the year as promised.
"We're confident that we will be able to make up but part of that is obviously then needing to ensure that we do find the four days in both (the) Senate and the House," he told ABC Radio.
"We'll be looking to find those four additional days and we'll have more to say about that in the coming days."
Opposition foreign affairs spokesman Simon Birmingham said the cancellation was part of long-established traditions.
However, he indicated the length of parliament's suspension could be re-examined.
"No doubt people will look carefully at these traditions in the future and assess how they carry forward in terms of marking significant occasions," he told ABC Radio on Monday.
"After a period like this, the United Kingdom system, the Australian system, all will have a look back at what has occurred through this period of transition, this period of mourning, and that will all feed into what occurs in the future.
"Now is a time where, I think rightly, nearly all politicians and public leaders are avoiding debate, controversy or otherwise - and that is at it should be."
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