School leaders from the National Union for Head Teachers (NAHT) said the tests were "harder than expected".
In a survey of 2,600 NAHT members, 98% said this summer's English spelling, punctuation and grammar test for 11-year-olds was "difficult", according to TES.
A third said the maths paper 2 for Year 6 pupils was “much more difficult than expected” and 24% said the same about the maths paper 3.
"Today's results cannot and must not be compared to data from previous years," Russell Hobby, general secretary of school leaders’ union NAHT, said.
"If they are, they will give a misleading picture of school performance."
Hobby reiterated that children who sat Key Stage 2 SATs this year are the first to be tested on the new National Curriculum.
"They have only had two years to master a curriculum which should normally be taught over a four-year period," he added.
"The government is proud to say this new curriculum is harder than in previous years, but seemingly happy to put these children at an automatic disadvantage.
"Added to this, the government has made serious mistakes in the planning and implementation of SATs this year, with delays and confusion in the guidance materials."
In the survey, 88% of respondents said they had “experienced issues relating to the difficulty of tests” and 81% said pupils had not had enough time to complete some of the Key Stage 2 tests.
Almost all (98%) said that this year’s Key Stage 2 SATs were not appropriate for children with special educational needs (SEN).
Education Secretary, Nicky Morgan reiterated what NAHT said regarding not comparing the results to previous years, telling the BBC: "They simply cannot be compared directly.
"Neither schools nor parents should try to compare this year's results with previous years.
"The tests are new and are based on a new, more rigorous national curriculum – based on the best evidence from across the world."
James Bowen, director of NAHT Edge said: “SATs have become a box-ticking exercise for children in order to satisfy bureaucrats and politicians.
"The poorly designed tests and last minute changes we have seen this year do not add value to teaching."
In May 2016, headteachers wrote an open letter to Nicky Morgan asking her to cancel the publication of any primary test results taken this year.
The NAHT argued the results were too “unpredictable”, because there was “inadequate time” to implement the new curriculum.
“Unfortunately, significant mistakes have been made in the planning and implementation of tests this year, with a negative effect on children’s education,” Hobby told The Huffington Post UK at the time.
“The tests are not seen as helping teachers to teach or providing reliable information to parents about the progress of their children.
“We want to find a clearer, simpler system that gives parents and schools the information they need to improve children’s learning.”