Mrs Riordan didn't want to comment on whether the orders should be extended to non-traffic related offences.
Nationally, more than $20million in unpaid traffic-related fines and reparations have been paid since it became possible for people to lose their licence for not paying up.
Justice Minister Amy Adams said the orders helped send the message it was not acceptable to ignore fines.
"The stop orders are working as intended," she said. "Rather than potentially losing their licence, people are choosing to pay their fines.
"The aim of [the orders] was not to take away people's drivers licences but to ensure that fines remain a credible sanction."
The nearly 19,500 people who had paid up included New Zealanders living across the ditch, she said.
"There has also been a significant response from people owing fines in New Zealand but are now living in Australia in response to us sending them the warning letters. These fines have either been paid in full or have made arrangements."
Nearly 12,000 warning letters have been sent to customers. Twenty-seven drivers currently have their licences suspended, while a further 11 drivers had had their licences suspended and then reinstated when the fines were paid.
An additional 1800 people had a DLSO status as they arranged to pay the fines.
Original forecasts estimated $7 million annually would be collected by the scheme. NZME.