But they said it would be reasonable to consider allowing Perth to borrow the ancient stone.
Deputy First Minister John Swinney, fellow SNP Perthshire MSP Roseanna Cunningham and SNP MP Pete Wishart are backing a plea by Perth & Kinross Council to have the stone as the centrepiece of a new museum and arts hub to be created in Perth City Hall.
And the group of senior public figures responsible for oversight of the stone announced they were holding a consultation on the proposal.
The stone - an oblong block of red sandstone measuring around 26 inches x 17 inches x 10.5 inches - was the coronation stone for Scottish kings for hundreds of years before being seized by the English in 1296 and installed in Westminster Abbey, where it has continued to be used at coronations, including the Queen’s in 1953.
But since 1996 - when John Major’s Tory government decided to return it to Scotland - it has been housed in the Crown Room at Edinburgh Castle, where it is displayed along with Honours of Scotland - the Crown, the Sceptre and the Sword of State.
Edinburgh Southern Labour MSP Daniel Johnson said the stone and the other regalia should be kept in the Capital - but suggested a loan to Perth could be considered.
“I don’t think we should be precious about it and there may be some merit in it being on shown in Perth,” he said.
“But the Stone of Destiny belongs with the Honours of Scotland and we don’t want to see them permanently separated.
“A loan and a temporary relocation might be acceptable, but I would want to see it back in Edinburgh after that.”
Lothian Conservative MSP Miles Briggs agreed the stone belonged with the other Scottish regalia.
“It makes sense for people to see them all together in one place and with the large number of people visiting Edinburgh Castle it seems the best place to have them.”
And he echoed the loan suggestion. “Perhaps Perth could borrow it for a bit.”
The Scottish Government announced yesterday that the Commissioners for the Safeguarding of the Regalia, who are responsible for the stone, were seeking views on its future location after receiving a proposal from Perth & Kinross Council and its delivery partner Culture Perth & Kinross.
The commissioners are the First Minister, the Lord Justice Clerk, the Lord Advocate and the Lord Clerk Register.
The deadline for comments is September 19. The final decision on any proposal to relocate the Stone will lie with the Queen, acting on the advice of the commissioners.
Mr Swinney, who is MSP for North Perthshire but was born in Edinburgh and went to Forrester High School and Edinburgh University, said the case for the stone being relocated to Perth was “very compelling”.
“The Stone of Destiny is widely regarded to have been quarried from Perthshire stone, and was used for the coronation of the Kings of Scotland at Scone for many years. It is therefore highly appropriate that the Stone should return to Perthshire.
“When the Stone was proposed to be moved from Westminster to Edinburgh Castle in 1996, I campaigned for its return to Perthshire. I am therefore delighted that a significant step has been taken towards achieving this goal.”
Perth & Kinross Council say the new museum in the former Perth City Hall is due to open in 2022, funded as part of the £700m Tay Cities Deal which has investment from both the Scottish and UK governments.
The council said: “There, the Stone of Destiny would be free to visit, in an accessible city centre public building two miles from its original home at Scone.
“At City Hall the wider significance of the Stone can be revealed by displaying it alongside one of the UK’s oldest and most important public collections.”
It said visitors would enter the centrepiece display, the Stone Pavilion, and be introduced to the stone with a short film telling its story from its mythic origins to its role in early kingship ceremonies and its role as a powerful symbol of nationhood and monarchy.
“After the film, visitors will see the Stone of Destiny. Displayed in a custom-designed secure case, the Stone will be animated with light and sound, recreating the 13th century crowning of Alexander III.”
Perth council leader Murray Lyle, said: “The Stone of Destiny is one of the UK’s most important cultural objects. Here in Perth we can display it in a context as close to its original home at Scone as possible and within reach of millions of Scottish people who live outside the central belt – meeting the aspiration of Scotland’s national heritage strategy to make our cultural heritage open to everyone.”
But Iain Whyte, leader of the Tory group on Edinburgh City Council, was sceptical about the Perth proposal to remove the stone from Edinburgh: “In that case, why not go the whole hog and take it to Scone?” he asked.
Edinburgh council Leader Adam McVey said: “We can see why Perth would want to host the Stone of Destiny - we’ve been its proud caretakers since it came home to Scotland more than 20 years ago.
“While this won’t be a decision for us to make, I know the Castle takes pride in being home to this incredible piece of Scottish history and culture and we will be keen to hear the views of the people of Edinburgh as this is considered.”