The CITB announced last month that it would be suspending levy collection for at least three months.
But the federation believes that does not go far enough to help aid cash-flow in the construction industry during the coronavirus crisis.
Chief executive Richard Beresford said: “It is highly likely that many companies will not survive this crisis and it is therefore our collective duty to do everything possible to protect as many construction businesses as we can.
“I am grateful for the temporary suspension that the CITB has announced in respect of collection of the 2020 levy but we must now go a step further”.
The CITB confirmed last week that it would be furloughing a number of staff.
No mention was made of pay cuts for senior management.