Speaking at the National Education Union (NEU) Conference in Liverpool yesterday, the Labour leader set out plans to scrap the "regime of extreme pressure testing".
Labour said the policy would relieve pressure on a schools system forced to cope with overcrowded classrooms, and an ongoing crisis in teacher recruitment and retention.
But Conservative Schools Minister Nick Gibb said abolishing the tests would be a "terrible, retrograde step" which would "enormously damage our education system, and undo decades of improvement in children’s reading and maths".
In his speech yesterday, Mr Corbyn said: "We need to prepare children for life, not just for exams.
"Sats and the regime of extreme pressure testing are giving young children nightmares and leaving them in floods of tears.
"I meet teachers of all ages and backgrounds who are totally overworked and overstressed. These are dedicated public servants. It's just wrong."
Primary schoolchildren undertake national tests and teacher assessments in English, maths and science at the end of Year 2 when aged six to seven, and national tests and teacher assessments in English and maths and teacher assessments in science at the end of Key Stage 2 (Year 6), aged 10 to 11.
Last year the Government announced that Key Stage 1 Sats would be replaced with a new baseline assessment in reception beginning in 2020.
Mr Corbyn also announced yesterday that the next Labour government will scrap baseline assessments for reception classes.
He said Labour would consult parents and teachers on an alternative that "prepares children for life, not just for exams".
Mr Gibb condemned the plan to end school testing, saying: “These tests have been part of school life since the 90s. They have been pivotal in raising standards in our primary schools. That’s why Labour governments led by Tony Blair and Gordon Brown supported them. ”
“Abolishing these tests would be a terrible, retrograde step. It would enormously damage our education system, and undo decades of improvement in children’s reading and maths. Labour plan to keep parents in the dark.
"They will prevent parents from knowing how good their child’s school is at teaching maths, reading and writing. Under Labour, the government would simply give up on ensuring all our children can read and write by the age of 11.”
But Dr Mary Bousted, joint general secretary of the NEU, said: "Jeremy Corbyn gets it - he recognises the damage that a test-driven system is doing to children and schools; he understands what needs to change; he sets out ideas for education which will make sense to parents and teachers."