The school has "a good sense" of the cause but has to wait until the joint police and fire service investigation has concluded, GSA director Tom Inns told MSPs.
He initially described the fire as an "accident" before correcting himself to call it an "incident", at Holyrood's Education and Culture Committee.
Around a tenth of GSA's historic Macintosh Building and a third of students' work - which was just hours from completion - was destroyed in the fire.
The fire broke out at around 12.30pm on May 23 and the deadline for the final year students' degree show work was 5pm that day, Mr Inns said.
The school had initially set a fundraising target of £1 million to restore the building but is now looking to raise around £20 million, he added
The GSA is currently involved in a "complex negotiation" with insurers but they will not fund the whole restoration, he told MSPs.
"We have been in discussion with the insurance company and a team of people appointed to deal with the immediate securing of the building, and the estimates are probably somewhere between £20-£35 million," he said.
"In terms of the actual accident - or the incident - itself that is still under investigation by the police and the fire service so they still haven't reported back on that.
"We have a good sense of what actually happened but there's certain details of that which are still unknown, and we will have to reflect on what actually happened with that particular incident."
He added: "The assessment process I think was going to get frozen at 5pm that Friday afternoon and that was when all the work was going to be inside the degree show spaces and then the assessment teams would be going in on the Monday."
All 102 students affected have since been assessed under "mitigating circumstances" and awarded their degrees.
They will also be able to bid for a share of the Glasgow School of Art Phoenix bursaries programme, to which the Scottish Government has committed £700,000. The programme will help students to recreate their work and recover from the setback of missing their final degree show, which would have been a key opportunity to showcase their work to galleries and collectors.
It will take 12 to 18 months to reopen the east wing of the building and 36 to 48 months to reopen the west wing, Mr Inns said.
He is "reasonably confident" they will be able to fully fund the restoration, he added.
"I say reasonably confident because there are unknowns in that because we have an insurance policy on the building - the building is well insured," he said.
"The insurance will cover certain things, it won't cover other things. Obviously it's a very complex insurance case.
"We will have to raise funds so we will be setting up a fundraising campaign, so I think if all of these things come together we will be able to cover the cost of that restoration.
"I am an optimistic person."
He added: "We originally marked the fund at £1 million, but bear in mind we marked that up on the Saturday after the fire but that was before we sat down and actually worked it out.
"We're going to formally launch the fund on Wednesday and we're looking to raise probably between £10-£20 million depending on what we will actually be needing to be reasonably comfortable with the situation.
"We've had some very generous contributions from individuals, one or two pledges from trusts and organisations but it's a bit too early to say exactly what that is, but I think we can be reasonably confident that if we worked that well and effectively we would be able to raise the funding.
"The Scottish Government said they will match-fund up to £5 million to support the restoration. There's no more detail from the UK Government."
Conservative MSP Mary Scanlon said: "The UK Government has said: 'We don't know the precise extent of the damage or what the costs will be so we can't put a figure on it, but we will make contributions in the millions if necessary'. So they're waiting for detail."