A consultation on the future of primary assessment published by the Department for Education today reveals plans to review the statutory status of Key Stage 1 assessments, also known as Sats.
The consultation document states that the move is intended to "reduce the burden of statutory assessment for teachers and pupils". A new assessment for pupils when they first start school is proposed instead.
Education Secretary Justine Greening said: "The government has reformed the primary school system to make sure children can master the basics of literacy and numeracy so they get the knowledge and skills they need to succeed in later life.
"Now we want to build on that by developing a stable assessment system that helps children learn, while freeing up teachers to do what they do best - supporting children to fulfil their potential."
Russell Hobby, general secretary of school leaders' union NAHT said the consultation was the result of months of detailed talks with the Department for Education.
"We appreciate the engagement of the Secretary of State with the concerns of school leaders," he said.
"The government has listened to many of the principles and recommendations contained in NAHT's independent assessment review group report. There's more to be accomplished but we've made good progress from where we were a year ago."
However, Kevin Courtney, general secretary of the National Union of Teachers, said that although Justine Greening appears to have listened to the sector on tests for seven-year-olds, he has concerns about testing for younger children.
"The consultation floats the idea that statutory assessment at Key Stage 1 will be set aside, but not until the early 2020s.
"This would be a welcome concession to the thousands of teachers who have protested against the effects of a test-driven curriculum on six- and seven-year-olds.
"But the relief that is offered at one stage of education is accompanied by changes for the worse for younger age groups. In a triumph of hope over experience, the DfE wants to reintroduce baseline testing to the early years, despite its failure in 2015/16."
A consultation on the proposals will run until 22 June.