Thousands of key stage two test papers are to be sent back by schools for re-marking.
The Times reports that over 100 schools have contacted the National Association for Head Teachers, a union representing those with jobs in education
, to say that they are unhappy about standards of marking.
Mick Brookes, the union's general secretary, told the paper: "Either reading has been marked too high or writing has been marked too low.
"Wherever we go, people are particularly incandescent about the quality of marking of writing," he added.
According to the Times, Mr Brookes is now calling on exams watchdog Ofqual to declare how many schools have appealed to exam boards.
While primary school staff
are already aware of how their pupils have done in the key stage two Sats tests, national results are due to be released today.
Recent reports have suggested that schools plan to boycott the exams following news that the government will abolish Sats tests for 14-year-olds.