A key crossbench senator has made his party's support for the Turnbull government's new bank levy conditional on the tax applying to foreign banks.

And the leader of the Nick Xenophon Team, Senator Nick Xenophon, has also flagged concerns about the government's decision to keep the proposed laws under wraps until they are introduced into the parliament.

But the push from crossbench powerbroker has been rejected by the government, with Finance Minister Mathias Cormann saying the major bank levy was designed to boost the competitiveness of smaller banks, including foreign ones.

Senator Xenophon told the ABC's Insiders program he supported the 0.06 per cent levy, which would apply to Westpac, NAB, Commonwealth Bank, ANZ and Macquarie and is designed to raise $6.2 billion, in principle but suggested the levy should be more broadly applied – and the extra money used to compensate victims of bank fraud.