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.