National ICAC a separate issue: PM

Prime Minister Malcolm Turnbull won't entertain the idea of a national ICAC in return for support from crossbench senators for his ABCC legislation.

PM Malcolm Turnbull says he's not committed to his government funding the full Gonski schools plan. (AAP) Source: AAP

Prime Minister Malcolm Turnbull says if crossbench senators want a national corruption commission they should put up a private member's bill - but that is a separate issue to restoring the construction watchdog.

Mr Turnbull needs the support of six of the eight crossbench senators for his Australian Building Construction Commission bill to prevent a double dissolution election on July 2, but some are pushing for a national independent commission against corruption (ICAC).

"Whatever the merits of that, that is quite separate and distinct from the ABCC legislation. If they want to have a federal ICAC they should move a private member's bill in the normal way," he told Sky News on Sunday.