He said the first cases for recall would involve a number of borrowers who were in Australia.
The bill also makes it easier for borrowers to manage and repay their loans through on-line services and a simplified system of penalty rules.
"This will eliminate much of the administrative complexity and confusing paperwork that has made things more difficult for student loan borrowers than they needed to be," Mr Dunne said.
"Most borrowers whose income is from salary and wages will benefit from a further simplification which removes the current annual end-of-year assessments or 'square-ups'."
Labour supported the bill but complained about the $40 administration fee for the new, streamlined service.
MP Grant Robertson said Inland Revenue was going to save money from the new scheme, and the administration fee was a revenue-gathering exercise.
The Union of Student Associations (NZUSA) said the legislation was a mixed bag - administrative changes were welcome but the new fee was "an unnecessary tax" on students.
- NZPA