The unusual move has been made by primary schools principals from a range of sectors across Northern Ireland.
In all, the 146 head teachers represent schools with a total of 38,808 pupils.
The letter has been sent to the secretary of state James Brokenshire, education officials and the leaders of the DUP and Sinn Fein, Arlene Foster and Michelle O'Neill.
The BBC understands that it was planned prior to last week's general election.
The principals also write that they want a guaranteed year on year increase to school budgets in line with inflation for at least the next five years.
The aggregated schools budget - the part of the education budget which goes directly to schools - was £1.16 billion in 2016/17.
A seven per cent rise in it would equate to around £80m.
In their letter, the principals say that the amount is needed "simply to maintain basic provision for the children in our schools."
"Schools across our country have, for many years, delivered a high quality education to all our children, in the midst of social and civil unrest, and within a very challenging financial context," they write.
"This high quality education and the high standards we achieve is now seriously at risk."
A number of principals have previously warned about the impact of a declining education budget in their schools.
In April, 43 said they would refuse to implement any more cuts to their school budgets.
However, this new letter is now backed by many more head teachers.
The Department of Education has also previously warned of "extremely challenging" financial conditions for schools.
Meanwhile, the former education minister Peter Weir also previously said that schools here needed an extra £240m over the next three years just to maintain spending at 2015/16 levels.
Over 140 principals have signed a letter demanding an immediate increase of 7% in school budgets.