The Prince and his wife Camilla, Duchess of Cornwall, joined Prime Minister Julia Gillard at the opening on Saturday of a terrace on the edge of Lake Burley Griffin in Canberra, named in honour of Queen Elizabeth II on her Diamond Jubilee.

Ms Gillard noted that not far from the terrace, which originally was Parkes Place, was the writing table on which Queen Victoria signed into law the Australian constitution.

“Today the symmetry is made complete with the naming of Queen Elizabeth Terrace,” Ms Gillard said.

The green space in front of Old Parliament House and two roads either side will now be named in honour of Henry Parkes, one of the fathers of Federation.

Later, in the company of Ms Gillard, Prince Charles met onlookers including Canberra woman Alyson Richards, who wore a T-shirt with an image of the Queen.

She caught Prince Charles’s attention and gave him a packet of Tim Tams.

“Happy birthday for next week,” Ms Richards said to him.

“You’re very kind,” Prince Charles replied. “What I’ve discovered is that you have to dunk them.”

Later Ms Richards told AAP, “I think he’s a real Aussie now.”

The royal couple then went to Government House, where Prince Charles and Camilla met briefly with Governor-General Quentin Bryce.

The Prince alone spoke with Ms Gillard and Opposition Leader Tony Abbott for about 10 minutes each.

“It’s a real thrill,” a visibly excited Mr Abbott said as he greeted the Prince.

Ms Bryce presented the royal couple with a gift the Australian people are giving to the Queen in celebration of her Diamond Jubilee.

It is a writing compendium made from the timber of a massive North Queensland figured butt maple tree.

During her chat with Ms Bryce, the Duchess expressed amazement that about 70 kangaroos lived in the grounds of Government House.

Prince Charles told a Government House lunch he was sad he and Camilla had not been able to see more of Australia, but was pleased to have caught a glimpse of “the extraordinary vibrancy of the multicultural society”.

Having met many emergency service volunteers at Sydney’s Bondi Beach on Friday, he said such people “provide the glue to such a diverse and energetic and determined society”.

“We shall leave here with great sadness that we can’t spend longer as we move to New Zealand, but taking with us such happy, special and amusing memories of all the wonderful people here,” he said.

Ms Bryce, who represented Australia at many of the Diamond Jubilee events in London, said what had touched her most deeply was “observing Her Majesty’s delight and happiness in every moment”.

“We are all seized with the historical importance of the 60th anniversary of Her Majesty’s reign,” she told the lunch.

“The significance of the Diamond Jubilee as a personal milestone is also very much in our hearts and minds.”

The royal couple’s final engagement was at the Australian War Memorial, where they laid a wreath at the Tomb of the Unknown Soldier, to the haunting sounds of a bugle.

Later they walked down the colonnade past the names of Australia’s war dead, inspecting the section which lists those who died in Afghanistan.

Prince Charles and the Duchess of Cornwall then boarded a flight to Auckland for the first leg of their New Zealand tour.