Jerry Lean, industrial relations director of the Construction Confederation, said Griffiths and Sutcliffe were keen to learn about the problems the industry faced.
He said: "The government is now aware of the industry's concerns and wants us produce hard evidence and examples of how and where the exploitation of foreign workers is taking place."
Both employers and the unions object to the government's interpretation of the European Posted Workers Directive's rules on workers' pay, which is that temporary foreign workers must receive at least the minimum wage.
Ministers want examples of how exploitation is taking place
Jerry Lean, Construction Confederation
It is understood that the union representatives at the meeting urged the government make it compulsory for firms to ensure all employees were treated in accordance with the industry's collective agreements.