Sir Fraser has attacked the SCIG, which comprises contractors, consultants and trade unions, after it proposed that an environment ministry be given responsibility for construction. Sir Fraser called instead for the industry to be placed within the Scottish Office's Business and Industry Department.
Sir Fraser's comments were made in his role as chair of the Scottish Construction Industry Pathfinder Group, which was set up by the Scottish Office as part of its consultation on how industry will fit into the new political arrangements.
Sir Fraser said: "Construction is a very important Scottish industry.
It employs more people than other industries such as oil, fishing and electronics that we hear so much about.
"It should be represented at the appropriate level within the Scottish Office to be in line with its importance as an industry." However, SCIG chairman Joyce Deans dismissed Sir Fraser's proposal and insisted that construction should be located within an environment department.
Deans criticised the Pathfinder report and reiterated the SCIG view that construction should be the responsibility of a housing and environment minister.
She said placing construction in an environment minister's portfolio would encourage the industry to think more about environmental issues when it was building new schemes.
Deans added that the SCIG did not believe construction should be grouped with industries such as textiles and whisky, two of Scotland's largest industries.
Construction in Scotland is currently part of the Scottish Development Department's portfolio and is overseen by MP Callum MacDonald, who is also responsible for housing and local government.
Deans blamed the Scottish Office for the wrangling over what department would be responsible for the industry, claiming that it had failed to clarify which departments would exist in the new parliament.
She said she wrote to the MP organising the structure of the new parliament, Henry McLeish, to seek clarification in January, but had not received a reply.
A Scottish Office spokesman said it was unable to comment on the issue in the run-up to the election.