The Duke of Edinburgh died in his sleep on Friday, two months before his 100th birthday and a short time after a month-long stay in hospital.

Australian Governor-General David Hurley, Prime Minister Scott Morrison and his wife Jenny, and NSW premier Gladys Berejiklian were among those who prayed for the royal family at St Andrews Cathedral in Sydney.

The Right Reverend Peter Hayward on Sunday gave thanks for Prince Philip's "extraordinary contribution" to the world.

"When he was a head boy at Gordonstoun (School), his final report said of him these words: 'Prince Philip is universally trusted, liked and respected. He has the greatest sense of service of all the boys in the school', and that was to define his life from then on," he said.

The Very Reverend Kanishka de Silva Raffel said Australians were deeply saddened by his death.

"On Prince Philip's many visits to Australia, we have come to know him as a man of compassion and service, personal warmth, intellectual curiosity and generous spirit," he said.

Speaking after the service, the prime minister said the prince embodied qualities the world desperately needed.

"Sure and steadfast ... he demonstrated that throughout his life, and we give thanks and give praise for that."

St Paul's Cathedral in Melbourne and St Peter's Cathedral in Adelaide will hold special services in coming days.

The duke's passing was marked with a 41-gun salute in Canberra on Saturday, in keeping with tradition being observed by other Commonwealth nations.

Flags were flown at half mast across the country and will be again next Saturday for Prince Philip's funeral in the UK.

Australians have sent thousands of condolence messages online via the government website pmc.gov.au, which will be forwarded to Buckingham Palace.

Former prime minister John Howard said the outpouring of support showed the country's love for the royal family, and that there is no movement for the country to ditch the monarchy and become a republic.

"Obviously the place and role of the monarchy has altered over the years... (but) I don't see any likelihood of change," he told Sky News on Sunday.

Prince Philip visited Australia 21 times, the first in 1940, before his marriage, as a midshipman aboard the battleship Ramillies.

Some of his trips to Australia drew international headlines for controversial comments.

On one occasion he asked an Aboriginal elder: "Do you still throw spears at each other?".

Mr Howard said it was his so-called 'gaffes' that made people, particularly Australians, warm to Prince Philip.

"He gave short shrift to political correctness when he encountered it, and that endeared him to millions of people," he said on Saturday.

Mr Howard was one of many past and present leaders in Australia who lauded Prince Philip as a man of great candour, wit and compassion who lived to serve others.

Former prime minister Tony Abbott, said the world seemed "a little emptier" after his death, while his successor Malcolm Turnbull shared how Prince Philip once identified him as "the Republican fellow" and then quipped: "You should have been a republic years ago!".

Australian Associated Press