Maori party co-leader Pita Sharples originally shared Mr Dunne's reservations, but is now supporting the bill.
However, he said he would push for teachers to have qualifications - the bill permits staff to teach without formal qualifications or without being registered with the New Zealand Teachers Council.
"We want people to have qualifications in some field or other; they [the qualifications] may not be in teaching, but they may be in other disciplines.
"It would have to be a qualification in whatever they are going to teach - something that qualifies them to teach it," Mr Sharples said.
He said he had not considered the impact of staff not being held accountable under the Teachers Council model.
When asked why he had changed his mind, Dr Sharples said: "because people have told me how it might work. Maori ... see it as a real possibility for developing a school that will produce quality students.''
Mr Dunne said he had relayed his opposition to Prime Minister John Key.
He said while United Future supported choice and flexibility within the education system, he had not been persuaded the charter schools' model was necessary or desirable to achieve that.
"The current system already provides for a significant range of schooling opportunities, and I cannot see there is a need to introduce the partnership schools approach to achieve the level of flexibility the proponents of partnership schools are seeking."
Labour's education spokesman Chris Hipkins said if Mr Dunne had pulled his support, then the Maori Party should do the same.
"Peter Dunne is right when he argues we don't need charter schools, that we already have a range of schooling options within existing legislation, and that the risks associated with charter schools are too great."
NZEI national president Judith Nowotarski said it was important charter schools did not become part of the education landscape in New Zealand.
"They will be bad news for children's education, particularly for those children who are struggling."