Glasgow Conservative MSP Adam Tomkins was speaking as Holyrood debated a report into the two blazes which devastated the building.
The renowned art school was extensively damaged in June 2018 while it was undergoing a £35 million restoration following a previous fire in May 2014.
The Scottish Parliament's Culture Committee has already criticised Glasgow School of Art for not giving enough priority to safeguarding the Mackintosh building against fire.
As MSPs discussed that report, Mr Tomkins backed calls from committee convener Joan McAlpine for a public inquiry into the fires.
He added: "The management of the Glasgow School of Art have proved themselves to be an unfit custodian of this national treasure and the public inquiry must consider whether the building and its future should be taken out of the GSA's hands and laid in some sort of public trust.
"The GSA management have not only allowed this iconic building to burn down twice in the space of four years, but in the aftermath of the 2018 fire they treated their neighbours, in the Garnethill community, both residents and businesses up and down Sauchiehall Street, with disdain and contempt."
He asked higher education minister Richard Lochhead: "When you put all of this together, is it not the minister's view that the time has long since passed for the Mackintosh building to be taken out of the hands of the GSA and placed into public trust?"
Mr Lochhead said there are "harsh lessons" to be learned for art school bosses, but he said they had taken steps to try to address some of the concerns of residents.
He went on to stress the building's importance as a teaching venue, telling MSPs: "It is important to remember the school is primarily a functioning higher education institution."
The minister said it is for art school bosses to determine how the historic building should be used in the future.
"The board has made clear its intention to rebuild the current site and that the Mack should return as a fully functioning art school," Mr Lochhead said
He went on to tell MSPs that the Scottish Government will decide if there should be a public inquiry after the Scottish Fire and Rescue Service publishes its report into the fire.
Pauline McNeill, Labour MSP for the Glasgow region, said the impact of the second blaze could not be underestimated, saying: "The community were totally devastated, and still are devastated.
"Families were split up due to difficulties in securing temporary accommodation. People were not allowed to return home for four months."
While she said the fire exposed "poor relationships between the local community and the Glasgow School of Art", she said these had been "poor for a long period of time".
Ms McNeill said: "If you ask any of the residents if they think there has been an adequate response from authorities, they'll tell you they felt abandoned by it.
"We must learn lessons, not just about the cause of the fire, but about the conduct of authorities."
Scottish Green Party co-leader Patrick Harvie said the Mackintosh fire should serve as a warning to other large-scale organisations which have an impact on their local community.
Mr Harvie read a written submission from neighbours of the Mackintosh building, who say Glasgow School of Art was a "selfish neighbour with little understanding of the impact they have on their community".
He added: "This is a warning to not just Glasgow School of Art, but to all institutions, all large organisations that have a role in shaping the nature of the community they live in and alongside.
"Build that trust before you end up encountering a crisis, because if you go through a crisis like the Glasgow School of Art has, it's too late to start building that trust then."