Pressure is growing on the Turnbull government over the Centrelink debt-recovery controversy, after the Commonwealth Ombudsman launched a wide-ranging investigation amid calls for the system to be shut down.

The ombudsman moved to initiate an investigation this month over significant concerns about automated data-matching processes being used to check welfare recipients' eligibility for some Centrelink payments, leading to outcry over the Christmas period as about 170,000 debt notices were issued.

Independent MP Andrew Wilkie and South Australian senator Nick Xenophon both referred the matter to the Ombudsman in December, but the investigation was already under way within the office.

Ombudsman Colin Neave confirmed on Monday he was aware of concerns raised about the automated data-matching system used by Centrelink.