A push to narrow the gap between mortgage rates offered to new borrowers and higher rates charged to loyal customers is shaping as a new threat to bank profits as the competition watchdog promises to target the issue and the government weighs a fresh inquiry into the banking sector.

The big four banks last week blamed falling profits from ultra-low interest rates for their decision to not pass on all of the Reserve Bank of Australia's quarter-percentage-point cash rate cut to home loan customers. The central bank cut the cash rate to a record low 0.75 per cent last week.