The contractor was working on a major restoration project when the inferno engulfed the site on Friday might.
It was the second blaze to hit the historic site in four years.
Glasgow MP Paul Sweeney told the Scottish Sun: “I think we need to ask hard questions about the judgement of the contractors and the governors at the school about whether they had the right processes in place and the right oversight.
“What was the contractor doing? Why wasn’t there CCTV, thermal camera or automatic links to fire brigade? I would have thought all of that would have been in place.
“We need to investigate exactly what the circumstances were and how the fire was able to get so badly out of control before anyone realised what was going on.”
A Kier spokesperson said: “An agreed fire safety strategy was implemented for the build phase of the Mackintosh restoration project, which combined measures for the protection of all those entering the site to work and to alert the authorities in the event of an outbreak of fire.
“These included a smoke and heat detection system and regular evacuation tests as well as 24 hour, 7 days a week security and fire warden patrols by a team of three guards, originally appointed by the client after the 2014 fire and subsequently by Kier.
“We continue to work with and support Scottish Fire and Rescue Service and our client as they determine the next steps for the Mackintosh building and site.
“We have a passionate team of local construction and crafts people, skilled conservators, supply chain and engineering specialists who have worked incredibly hard on this iconic landmark, and together we are all keen to do whatever we can to help moving forward.”
If the fire ravaged building can be saved from demolition it is believed restoration work this time around will cost at least £100m.