The churches said they wanted to have a meeting with the government to discuss the schools' future.
The schools have been dogged by controversy over their management, financial problems and performance.
Minister of Education Hekia Parata has made an interim decision to close Turakina Māori Girls College, which is one of only six remaining Maori boarding schools.
That prompted Minister of Maori Development Te Ururoa Flavell to criticise the churches for not fulfilling their obligations by upgrading them and making a bigger financial contribution.
But the Anglican church's Te Aute Trust Board chairman Stephen Jacobi said Mr Flavell has got it wrong.
"Rather than just criticising the churches for not doing enough, the government needs to be a partner in working out what the future of these schools is.
"Now I know that parts of the government system are very focused on that and we've had very good cooperation from government agencies around the future of Te Aute and Hukarere, but I don't think it's simply a matter as the minister was suggesting leaving it all up to the church."
Mr Jacobi said the church had poured $15 million into securing the future of Te Aute and Hukarere, and while the schools have integration agreements with the government, it can not do it alone.
"It's not just the responsibilities for the boarding hostels, the churches are responsible for the resources of the whole school.
"The government provides funding for the teachers and some funding for the maintenance of the buildings - very limited as I indicated, but it's not just about the hostels. It's about the whole thing - it's a shared governance around the whole school."
Mr Flavell said if the churches wanted the schools to flourish they had to increase their financial contribution, but MrJacobi warned that was not practical.
"That's going to be very challenging for many churches, and I think even the Anglican church, which has given so much in the last couple of years, will have to realise there are going to be some limits on this.
"That's why we need that closer partnership with the government and a very simple example is this: the amount of money we receive from the goverment in respect to Te Aute barely pays for the maintenance and upgrade of our swimming pool every year. So I really think the government and churches together need to find a better solution about working out a future for these schools."
Presbyterian Church's Maori Synod and Turakina's Board of Proprieters chairman Reverend Wayne Te Kaawa agreed with Mr Jacobi that the government needed to share more of the responsibility for keeping the schools open.
He believed a meeting with the government was long overdue.
"We definitely do totally support that idea. Government needs to be at the table, church needs to be at the table, whanau need to be at the table, iwi need to be at the table."
Mr Te Kaawa said a hui to discuss the future of Maori boarding schools on 6 November had to be cancelled, when the government asked that submissions in support of Turakina remaining open were delivered by that date.
Ministry of Education's deputy secretary for education system performance Andrea Schollman said state-integrated schools received funding that closely matched that received by state schools, and most state-integrated schools managed well on their budgets.
She said Te Aute and Turakina College's financial difficulties were due to the small number of students each school had.
"Both schools are appropriately funded. In the case of Te Aute and Turakina college, in 2014 the schools were funded at a rate of approximately $18,000 per student.
"In comparison, the average across across all state and state integrated secondary schools for operational funding and payment of teacher salaries was $7,600 per student.
"The key difference in the funding arrangements is that the Proprietors of integrated schools are responsible for the provision of school property and own the property."
A spokesperson for Minister of Education Hekia Parata said she was unavailable for comment, but was "sure she'll consider a request for a meeting if she receives one".