The prime minister had a private audience with King Charles at Buckingham Palace in London on Tuesday, local time, ahead of the coronation at the weekend.
"It was a pleasure to meet King Charles III again at Buckingham Palace and an honour to represent Australia at his coronation," Mr Albanese said in a tweet after the meeting.
Mr Albanese reiterated during the audience that the King and other members of the royal family were welcome to visit Australia.
The prime minister is among a contingent of Australians invited to the coronation along with Governor-General David Hurley and state governors.
In an interview with broadcaster Piers Morgan, Mr Albanese said he would do "what is entirely appropriate as the representative of Australia" when asked if he would swear the oath of allegiance to the King.
Members of the public watching the coronation have been asked to join the oath of allegiance, but several prominent government ministers have said they will not take part in the pledge.
Treasurer Jim Chalmers said he was "unlikely" to pledge allegiance to the King during the coronation or watch the ceremony.
The Australian Republican Movement had called for Mr Albanese to stay silent during the oath.
Mr Albanese told Morgan he had a lot of respect for King Charles despite being a life-long republican, adding that he didn't expect to see an "imminent" referendum on removing the monarch as head of state.
"When the demand is there, I'm sure a vote will be held," he said.
The Australian delegation set to attend the coronation includes Matildas captain and football star Sam Kerr, singer Nick Cave, Aboriginal artist Jasmine Coe, comedian Adam Hills and London-based nurse Emily Regan.
In honour of the coronation, the Australian government will contribute $10,000 to the Western Australian conservation charity Friends of the Western Ground Parrot.
Mr Albanese said King Charles had long championed conservation and the government was pleased to mark the event by helping to protect the critically endangered bird.
The King, who is the monarch of 14 overseas realms including Australia, will host a lunch for prime ministers and governors-general at Buckingham Palace and also attend a Commonwealth Heads of Government Meeting on Friday, the day before his crowning.
Mr Albanese said he would be "meeting with other world leaders to strengthen Australia's relationships around the world" during his visit to the UK.
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