Catholic school principals says the government's national standards in reading, writing and maths are contrary to social justice, fairness and equality.
The Catholic Primary Principals Association, which represents 200 Catholic principals, has passed a motion condemning the standards, saying they do not recognise the dignity and sacredness of every student.
It says this is out of step with the special character of Catholic schools, which value equality and social justice.
The association has opposed the standards since last year, but has not spoken publicly against them until this week.
Its president John Coulam says teachers are too over-worked to implement the standards properly.
He also says the standards have been hurried and will disadvantage some children.
But Education Minister Anne Tolley says the standards are already identifying children who need more help.