He said: "Every five years parliament debates whether we should carry on at all, and every 12 months both houses in the parliament debate and then vote upon the approval of our levy scheme."
The row arose after Prescott made a speech at a Guardian/Observer housing conference last month, in which he said: "It's a damn disgrace the construction industry hasn't produced the skills that it needs."
He added that construction was one of the few industries with a levy-based training scheme, and he said it didn't work well.
In the letter, Latham said that when the CITB put its case to parliament it had to have had any proposed increases approved by the industry.
He said he had written to Prescott asking for a meeting so he could give him more details about out the work of the CITB.
Latham said he had outlined some of the board's achievements in the letter. He said he noted that the CITB was the largest single provider of health and safety training to the industry, and that it was at the centre of debate about encouraging the recruitment ethnic minorities and women.
Building readers responded to Prescott's attack with an overwhelming demonstration of support for the CITB.
One letter of support from Ian Davis, the director general of the Federation of Master Builders, said training for small and medium-sized builders would collapse without the CITB.