Chief Secretary to the Treasury Danny Alexander said Westminster would give "millions", if necessary, towards the reconstruction of the world-renowned Charles Rennie Mackintosh building.
The Scottish Government has already said it will do all it can to assist in the rebuilding of what is regarded as one of the finest architectural works in the UK.
Fire chiefs are making a full assessment of the damage following yesterday's blaze but suggest that around 90% of the building has been salvaged and up to 70% of its contents are safe.
The fire service has yet to confirm the cause of the blaze, which some students have suggested started in the basement when a spark from a projector caught a piece of foam.
Speaking in Glasgow today, Mr Alexander said: "It's a hugely important building not just for Glasgow and Scotland but for the whole of the United Kingdom.
"I can tell you that the UK Government will be willing to make a significant financial contribution towards the cost of rebuilding.
"Obviously at the moment we don't know the precise extent of the damage or what the costs will be, so I can't put a figure on it, but the Chancellor and I have spoken this morning and we both think it is appropriate."
Pressed on what the UK contribution would be, Mr Alexander said: "We could make contributions in the millions if that is necessary."
Scotland's Education Secretary, Michael Russell, said earlier: "My thoughts are with the staff and students of Glasgow School of Art at this distressing time.
"The Scottish Government will do all it can to help the school rebuild and to ensure that all those students affected are supported and can continue with their studies."
Smoke could still be seen rising from the charred windows of the school today, 24 hours after the flames took hold.
Students were busy putting the finishing touches to their work in preparation for the art school's annual degree show when the fire broke out at around 12.30pm.
No-one was injured in the fire but students, art lovers, architects and Glasgow officials spoke of their sorrow at seeing the "iconic" building in flames.
As well as housing one of Europe's leading art schools, the listed Mackintosh-designed building is a tourist attraction in its own right.
Completed at the turn of the 20th century, it was voted as the best building of the past 175 years in a poll by the Royal Institute of British Architects (Riba).
President Stephen Hodder said: "Damage to a building of such immense significance and uniqueness is an international tragedy. It is irreplaceable."
The Scottish Fire and Rescue Service said work is continuing to save and protect the building and its contents.
Assistant chief officer Dave Boyle said last night: "We are of course very conscious the Mackintosh is a world-renowned building that is a key feature of this great city, and that the artworks it stores are not only valuable but also cherished.
"We are acutely aware this period is the culmination of years of endeavour for students and that their irreplaceable work is inside the Mackintosh.
"Work to save everything that can be saved is ongoing and we will continue to work closely with GSA staff and students throughout this operation."