There is "no good reason" why the Department for Education can't "plainly say" that Sats must be cancelled this year, teachers have said.
The DfE has remained silent on plans for the primary tests following last night's announcement that schools must close to the majority of pupils.
Now the NEU teaching union has warned that the delay "just adds to the suspicion that yet again the government is intending to impose its own warped sense of priority on schools".
Tes asked the department this morning about plans for the 2021 Sats, but it had failed to respond by the end of the day.
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Mary Bousted, joint general secretary of the NEU, said: "There is no good reason why the DfE can't say plainly and simply that this year's Sats are cancelled.
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"Delay just adds to the suspicion that yet again the government is intending to impose its own warped sense of priority on schools.
"This summer, schools will be totally committed to helping pupils who will have experienced more than a year of learning disruption. Sats, with all the extra pressures they entail, are the last thing that schools need."
Last month it was announced that the government had U-turned on its plan to press ahead with all primary assessments in 2021, cancelling key stage 1 Sats and some of the Year 6 tests.
However, the DfE said the majority of key stage 2 Sats would go ahead in the summer, despite repeated calls for the tests to be scrapped.
The current plan is for KS2 Sats papers in reading and maths, as well as the Year 1 phonics check, to take place in 2021.
But after the prime minister announced that schools must close to the majority of pupils last night and the cancellation of "normal" GCSEs and A levels, the DfE has remained silent on whether the plan for Sats has changed.
Paul Whiteman, general secretary of school leaders' union the NAHT, which has called for the 2021 tests to be scrapped, said: "In light of last night's announcement, we would expect the government to cancel statutory tests in 2021. Students have faced, and will continue to face, significant disruption to their learning this academic year. Last night's announcement only further reinforced that.
"We really can't see that there's any other option for the government now than to cancel Sats for 2021."
He added: "Students have faced significant disruption to their learning this academic year and sadly that does not look set to change any time soon. Sats would only take time away from valuable face-to-face teaching and distract from the effort to support young people's wellbeing and mental health."
A spokesperson for the anti-Sats campaign group More Than A Score said: "The government must urgently give primary schools and Year 6 pupils reassurance that Sats will not take place in May.
"At the moment, 10- and 11-year-olds are the only pupils facing tests under exam conditions in the summer term. These children have been in school for a maximum of 15 weeks since March 2020; many spent a portion of the autumn term self-isolating.
"There is no place for government tests in this academic year. Pupils across the country are further from a level playing field than ever. The last thing they need is the threat of high-pressure tests in four months' time. Going ahead would be morally and ethically wrong and risks causing more harm to mental health and wellbeing.
"Sats are not the way to assess the effects of Covid on pupils and schools, despite what the government claims. The tests are designed to measure school performance, not to diagnose learning gaps. Schools already know where those learning gaps are. Even in the most difficult circumstances, they are doing everything they can to help children bridge them."