While Remembrance Day is still around the corner, flags across the country have been lowered to honour one of Australia's former governors-general, Sir Ninian Stephen, who died on October 29.

A state funeral service for Sir Ninian was held on Wednesday morning in Melbourne at St Paul's Cathedral.

In Australia, flags are flown at half-mast as a sign of mourning, including after the death of a distinguished Australian citizen. While former and current governors-general automatically make the list, a spokeswoman for the Department of Prime Minister and Cabinet confirmed former prime ministers were also honoured in this way, such as Malcolm Fraser most recently in 2015.

Prime Minister Malcolm Turnbull paid tribute to the "great statesman" Sir Ninian, declaring there were "very few honours [he] doesn't have to his name".

"He's been knighted five times, was a Justice of the High Court of Australia and Supreme Court of Victoria, member of the Privy Council and Australian Ambassador for the Environment," Mr Turnbull said in a statement.

Sir Ninian was born in Britain and arrived in Melbourne in 1940, becoming Australia's only immigrant governor-general in 1982.

The flag will remain at half-mast all day on Wednesday at buildings occupied by the government and its agencies, whether in Australia or abroad.

"Other organisations are welcome to participate," the Commonwealth Flag Officer said in a statement.

Officially, circumstances when direction will be given by the government for flags to flown at half-mast include:

Flags in any locality can be flown at half-mast when a local citizen dies, or on the day of their funeral.

But the flag should never be flown at half-mast at night even if illuminated, the Australian government advises.

The last time flags were flown at half-mast nation-wide was Anzac Day this year.