King Charles III was on Wednesday presented with symbols of his authority in Scotland, two months after he was officially crowned as monarch.

The 74-year-old head of state received the Honours of Scotland -- a crown, sceptre and sword of state -- at a service in Edinburgh's St Giles' Cathedral.

Charles and his wife Queen Camilla are in Scotland as part of a week of official engagements, staying at their official residence the Palace of Holyroodhouse.

Crowds watched as they made their way by car to the cathedral but the couple were also met by groups of anti-monarchy protesters, shouting "Not my king."

Republican demonstrators have trailed Charles since his accession in September last year, as part of their campaign for an elected head of state.

There was controversy at his coronation, when police used pre-emptive powers to arrest a number of demonstrators, causing a row about free speech.

The service of thanksgiving and dedication was attended by Charles's eldest son and heir Prince William and his wife Kate, and other senior royals.

Scotland's First Minister Humza Yousaf was in the congregation, despite the Scottish National Party (SNP) leader being an avowed republican.

But several Green lawmakers in Yousaf's governing coalition in the devolved Scottish Parliament stayed away, as they oppose hereditary monarchy.

One of them, Patrick Harvie, said the monarchy was "fundamentally at odds with the kind of modern and democratic society we are trying to build here".

The SNP and Greens are pushing for Scottish independence but their bid to break away from the United Kingdom has received a setback in the courts.

The service came after a "people's procession" of prominent figures in the world of Scottish arts, politics, education, civil society and business.

Soldiers in regimental tartan kilts marched on foot up the cobbled Royal Mile to the skirl of bagpipes.

They were led by Shetland pony Corporal Cruachan IV, the regimental mascot of the Royal Regiment of Scotland.

A fly-past by the Royal Air Force aerobatic team the Red Arrows ended the celebrations.

Charles's mother, Queen Elizabeth II, died at the royal family's private Scottish Highland retreat, Balmoral, in September last year aged 96.

Her body was brought to Edinburgh and lay in state at St Giles' Cathedral, before being flown south to London for a state funeral. (AFP)