He said: "My aim is to dramatically increase the number of contractors that are signed up to the scheme, but this is going to take time." He added that he would be addressing a series of quality mark roadshows across the country.
Griffiths said that he was looking to work with the industry to design a straightforward accreditation scheme, and that he wanted to remove entry barriers.
In an interview with Building he said: "For the vast majority of firms working in the domestic market, there is no deterrent to join the quality mark as it is free."
In fact, the scheme is free only for contractors with a turnover of less than £1m, but Griffiths would not be drawn on whether this figure would be raised to attract wider contractor support.
The minister added that he was hoping to cut down on the red tape that contractors faced in joining client vetting schemes such as quality mark and Constructionline, the approved list that public sector clients are supposed to use.
Griffiths is also keen for British workers to help repair worn-torn countries such as Iraq. He said that Britain has many foreign workers employed in its industry, and that British workers should be reciprocating by helping to rebuild other countries.
He dismissed claims that non-English speaking workers were causing problems in the UK construction industry. He said he had seen no evidence to suggest that foreign workers were increasing the number of accidents on sites.