Queen Mary and King Frederik of Denmark arrive in Melbourne

Danish King Frederik and Australia-born Queen Mary have arrived in Melbourne for the first of two days of royal engagements in the city focused largely on renewable energy and sustainable development opportunities.

The pair's first official engagement saw them meet with the Victorian Governor Margaret Gardner at Government House on Tuesday morning.

King Frederik and Queen Mary signed an official visitors' book before posing for photos with Professor Gardner, her partner Professor Glyn Davis and Victorian Premier Jacinta Allan.

"We have exciting days ahead," the king said, adding that he was looking forward to this part of the tour.

In a business reception held afterwards in the Government House ballroom, Professor Gardner began a speech by detailing links between Australia and the Danish monarchy dating back to Australia's federation in 1901.

"One hundred and twenty-five years later and our nations are among the oldest continuous democracies in the world," she said.

"Our instincts for fair representation and strong civil liberties have served us well.

"And though our lands are separated by many miles and many great oceans, we find in each other suitable partners and continue to grow ever closer."

As well as seeking opportunity in their resources, the two countries were also underpinned by a belief in opportunity for all, the governor said.

"I know the Danes have a word — hygge — that speaks to a feeling of comfort and familiarity," Professor Gardner continued.

"In our context, we speak of our easygoing formality, a meeting between equals. Here we might say, 'No worries mate'."

King Frederik told the ambassadors, diplomats and business leaders gathered that "partnering for a green, secure and sustainable future" would be the theme of the reception.

"Queen Mary and I hope that many new, possibly historical outcomes will materialise between Denmark and Australia as an outcome of our visit here in Melbourne," he said.

"Turning sustainability into good business is a powerful driver.

The business reception was followed by a meeting with about 10 Danish companies with economic ties to Australia.

'Much we can learn from each other'

Queen Mary and King Frederik then visited the suburb of Prahran in Melbourne's inner south, where they toured a social housing precinct being redeveloped with Victorian Housing Minister Harriet Shing.

"It was a great way to start this event by walking around a little bit of Prahran to get an understanding of what's changing and the ambition for the area," Queen Mary said.

"And it's actually my old hometown — I lived here for three years."

Queen Mary then spoke to an audience about construction, sustainable development and urban renewal in Denmark, a nation regarded as a leader in sustainability.

"Every time waste becomes a resource and something new is built with something old, we extend the life of not only our buildings, but the life of our culture, our shared heritage, and, ultimately, of our planet," she said.

"Denmark and Australia share a common ground in many areas, and there is so much we can learn from each other.

"And together, we can continue to build and shape cities that honour both our past, but also take a responsibility for the future."

Soon after, the royals graced the Melbourne Cricket Ground (MCG) playing field. There they chatted with two AFL club presidents, Hawthorn players and a few lucky Auskick participants.

Her majesty received a hearty cheer when she booted a football through the goalposts, before delivering a decent impression of a goal umpire’s two-handed goal signal.

Tasmania trip to conclude six-day visit

The Danish royals arrived in Australia on Saturday for their six-day visit, Denmark's first state visit in 40 years, with Uluṟu in Central Australia the first stop on the itinerary.

The couple then flew to Canberra on Sunday, where they received a ceremonial welcome at Government House and a state dinner attended by the prime minister, governor-general and opposition leader. 

On Monday, their majesties visited the Australian War Memorial in the nation's capital.

It is the couple's first official visit to Australia since Frederik ascended to the Danish throne in January 2024, and their fourth official visit to Australia together, with the last visit in 2013.

Karin Monk, a longtime committee member of the Danish Club in Melbourne who met the royal couple on their last visit, described their majesties as "interesting and interested" people.

King Frederik was "the people's king", Ms Monk said.

"He's into the people in the street. He really loves to engage in that sort of way," she said.

After their engagements in Melbourne, King Frederik and Queen Mary, who was born in Tasmania, will fly to Hobart on Thursday.