School groups fear news organisations want schools' results in the national standards in reading, writing and maths so they can compile league tables.
The Principals Federation and primary school union the Educational Institute say they believe the information will be used to rank schools.
They say that is not a good idea because there is little consistency between schools' judgements for national standards.
They also warn that in other countries league tables have prompted schools to narrow their teaching strictly to the basics.
The Principals Federation says it is considering how it might block league tables and the Educational Institute says the government should reconsider changing the law to stop the ranking.