King Charles III has pledged he will “seek always the welfare of our country” as he addressed Scotland’s nationalist-led parliament for the first time as monarch.

In a short ceremony at Holyrood – a motion of condolence to mark the Queen’s death at Balmoral last week – the King said his mother “found in the hills of this land and in the hearts of its people, a haven and a home”.

Charles said he mourned a life “of incomparable service” but would, he said, strive to follow his mother’s “inspiring example” of public duty.

“I take up my new duties with thankfulness for all that Scotland has given me,” the King said. “With resolve to seek always the welfare of our country and its people and with wholehearted trust in your goodwill and good counsel as we take forward that task together.”

His appearance was part of an intensely emotional day for the King, which began at Westminster with an address to MPs and peers with a similar pledge of “selfless duty”.

In Edinburgh several hours later, he had walked more than a kilometre through the medieval old town behind the Queen’s hearse, from the royal family’s official home in Scotland, the palace of Holyroodhouse, to a service at St Giles’ Cathedral. The queen’s coffin will lie at rest in the cathedral overnight until late on Tuesday afternoon, to allow mourners and well-wishers to pay their respects.

With former first ministers and former presiding officers watching from the public gallery, including Alex Salmond, Lord Steel and Lord McConnell, the King said he knew the parliament and Scottish people “share with me a profound sense of grief at the death of my beloved mother”.

He announced that his previous Scottish title of Duke of Rothesay would now pass to his son, Prince William.

Nicola Sturgeon, the first minister, said the Queen’s death was a moment of “profound sorrow” for many Scots. She had set an “extraordinary example to all of us”. The Queen had offered her “words of wisdom, counsel and humour that will stay with me for the rest of my life” during their private audiences at Balmoral.

The Scottish government, run by Sturgeon’s Scottish National party in partnership with the pro-independence and republican Scottish Greens, hopes to hold a second independence referendum next year.

The Scottish Greens’ co-leader, Patrick Harvie, a junior minister in Sturgeon’s government, appeared to hint at that goal when he urged the King to preside over a period of radical political and social change as monarch, paralleling the “extraordinary progressive change” seen during the Queen’s reign.

Harvie, who had not taken part in Sunday’s proclamation of King Charles’s reign at Holyrood, avoided any direct reference to republicanism. “As King Charles III begins his reign let us hope, indeed redouble our determination, that he will have the opportunity to witness change just as transformational, and more,” Harvie said. “It is needed.”

In an anecdote that brought laughter from the King, Sturgeon recalled one dinner at Balmoral when the lights in the room began flickering. Her husband, Peter Murrell, suddenly bolted from his chair to stop a young corgi, Sandy, eating through an electrical wire.

In 2014, she had a long journey down the new Borders rail line from Edinburgh to Tweedbank solely in the company of the Queen and Prince Philip. That had been “one of the greatest privileges of my life”, Sturgeon said.