Denmark’s new Australian-born Queen Mary has delivered a masterclass in looking stylish in icy conditions on her first full day in her new role.

Tens of thousands flocked to see her husband Frederik inaugurated as Denmark’s King on Sunday after his mother Margrethe II, 83, abdicated following a 52-year reign.

The royal couple made their first public appearance on a chilly -2C Copenhagen morning on Monday, attending the Danish parliament for a reception in their honour.

Moments before the couple and their eldest son Crown Prince Christian arrived in a Rolls-Royce known as Big Crown, parliamentary staff were frantically sweeping snow off the red carpet.

Mary, 51, wore a smart navy skirt and blouse ensemble with matching heels, clutch, leather gloves and a feathered hat, while her husband had donned a suit.

Parliamentary Speaker Soren Gade gave her a posy of pink flowers before she climbed the steps and greeted her mother-in-law Margrethe and brother-in-law Prince Joachim with a kiss on the cheek.

An Australian TV reporter asked if she had a message for her homeland, but Queen Mary did not respond.

The royal couple briefly posed for photographers and waved at a small crowd of onlookers before heading inside to the parliamentary chamber.

Up in the gallery, Mary smiled and sat in the middle of her son and husband looking down at MPs as the speaker hailed a new era for the Danish kingdom.

”I have great faith that King Frederik will be an excellent king for the entire Commonwealth – Denmark, the Faroe Islands and Greenland,” Mr Gade said.

”And by his side, the King has a wise and respected wife in Her Majesty Queen Mary.”

Danish Prime Minister Mette Frederiksen also heaped praise on the kingdom’s new Queen.

”The King has invaluable support and inspiration from his wife. And Denmark has a diligent, gifted and extremely poised Queen Mary,” Ms Frederiksen told the chamber.

Later the Danish National Girls Choir, wearing dark blue dresses, entered the floor of parliament and sang In Denmark I Was Born, a famous song written by Hans Christian Andersen.

The royals attended a reception with MPs and the prime ministers of the Faroe Islands and Greenland.

A day earlier, tens of thousands had turned out in chilly conditions to catch a glimpse of the royal family on a parliamentary balcony following Frederik’s proclamation.

Brisbane biomedical science university graduate Ebony Wilson, 25, and her grandmother Judy bought a last-minute plane ticket for Copenhagen on Wednesday to be part of the moment in history.

“I was thinking about it and then I thought, why not be spontaneous? It’s a once-in-a-lifetime opportunity,” Wilson told AAP in Copenhagen.

Hundreds of Aussie expats on the Australian embassy’s email database affectionately known as the “Vegemite List” joined ambassador Kerin Ayyalaraju for a soiree to toast Mary’s promotion.

Mary wore a white dress by Danish designer Soeren Le Schmidt and appeared alongside the King and their four children Prince Christian, 18, Princess Isabella, 16, and twins Prince Vincent and Princess Josephine, 13.

The family has made repeated visits to Australia, including Mary’s home city of Hobart.

Australian Prime Minister Anthony Albanese described Queen Mary’s ascension as a “great day”.

“She has carried herself in a way that I think just brings enormous support and pride to all Australians,” he told ABC Radio.

Mary and Frederik met at a Sydney pub in 2000 during the Olympic Games.

-AAP