Mrs Bennett said 58 per cent of people with outstanding warrants clear them within 28 days. The new rules would given them an extra 10 days to clear or challenge the warrant before their benefit is stopped.
Mrs Bennett said the policy, which had a "minimal" $139,000 annual administration cost, was about people doing the right thing and coming forward to authorities.
She said it was not beneficiary bashing.
Green Party co-leader Metiria Turei said the policy was a distraction and was deliberately released on the last day of the Public Health Association's conference on inequality and child poverty in Wellington.
"It is dog whistling, and typical tactics from Paula to try and avoid the real issue of child poverty, which as Minister of Social Development she has a responsibility for addressing, but is refusing to do so."
The policy would make no difference to those on the run from police, as they generally would not be meeting their Work and Income obligations, Ms Turei said.
"This whole illusion of toughening up is just that, an illusion. This is a stunningly useless distraction to avoid the Government's failures."
