The Turnbull government will break through the country's former debt ceiling this week, breaching the $500 billion mark as it doubles the credit card bill it inherited from Labor.

On Tuesday, gross Commonwealth debt reached more than $499 billion, after growing by more than $2 billion since Friday and $9 billion since early May.

The record level of debt has sparked calls from within the Turnbull government and the Senate crossbench to restore the formal debt limit abolished under a deal struck between the Coalition and the Greens in 2013.

Under current regulations, Treasurer Scott Morrison only has to request the Australian Office of Financial Management to raise the gross debt limit, the total face value of government securities on issue.