Centrelink's contentious debt recovery system is making some of the targeted people feel suicidal, independent MP Andrew Wilkie has claimed, as the furore over the clawback persists despite the government's insistence it is working exceptionally well.

The Tasmanian MP said the Commonwealth Ombudsman had agreed to his request to look into the matter, which has come under criticism from the Labor Party and others for targeting some innocent recipients of social security payments with a flawed data-matching calculation, sometimes years after payments had been received.

"I've had people who have approached me who have been frightened, absolutely scared, people who are paying this money because they are so frightened by this very official letter," Mr Wilkie said on Wednesday.

"I've had four people now approach me in my office who I would describe as presenting as suicidal and in all those cases we've taken what action we thought was appropriate."