That will mean they will refuse to take measures like laying off staff to save money, even if it pushes them into a deficit.
A letter was sent out to all the parents of their pupils.
They said the situation facing them is "untenable" and is "seriously compromising their pupils' education".
They have also written to the Department of Education, the Education Authority and the secretary of state with the same message.
The letter, sent on Thursday and Friday, is signed by principals of 43 primary schools.
It said that it is "impossible for many schools to make further staffing cuts without seriously compromising their children's education. This is untenable."
The principals go on to write that they will manage their budgets carefully.
"We will not, however, facilitate any further cuts to our school budgets that will have lasting impacts on our pupils' education and well-being," they continue.
"Consequently, we will be planning for deficit budget positions."
The principal of the 470-pupil Stranmillis Primary School in south Belfast, Jackie Wallace, is one of those who have signed the letter.
"My job is to meet the educational needs of the children," Mr Wallace said.
"When the department give a meaningful and sensible budget that we can implement and still deliver quality education we will, of course, do that and we always have - we've always lived within our budget.
"But the current budget that's being delivered to schools is totally inadequate."
More than forty headteachers in greater Belfast have said they will refuse to implement any more cuts to their school budgets.