A review of testing today left the door open for primary school Sats to be scrapped in the future, in favour of teacher assessment.
An expert group, set up by Schools Secretary Ed Balls to look at the assessment system, recommended that national science tests for 11-year-olds be abolished, and that English and maths tests remain.
But in a statement the group said that ministers "should continue to invest in, strengthen and monitor the reliability of teacher assessment to judge whether a move away from externally marked national tests might be viable at a future date".
Group member Sir Jim Rose said: "Clearly if you had a situation where you had teacher assessment that was so robust that you were confident the information it was delivering was as good, or better, than national testing, then wouldn't you go for it?
"Meanwhile, you would want to run both together wouldn't you? It's a belt and braces job."
Today's report also calls for the Key Stage 2 tests in English and maths, which are taken by children in their final year of primary school, to be moved from May to June.
But this will mean that the results will not be available until the following September - after the children have started secondary school.
The review group's report says: "Secondary schools planning for their new intake of year 7 pupils should be based on teacher assessment data."
Group member Gill Mills suggested that in the future Key Stage 2 tests could become more like those taken by seven-year-olds at the end of Key Stage 1.
Those tests are taken at any time of the year, are not time limited or taken under exams conditions, and are marked by teachers. They are then externally moderated.
She said: "That's a good example of what's happening to move towards."
The group backed "single level tests" in English and maths, which are taken by pupils when teachers feel they are ready.
These tests are currently being trialled, and the group said that the third year of piloting will be needed before any firm judgments can be made.
It also endorsed Mr Balls's plans for school report cards, which would give details on how a school is performing in exams, as well as other areas such as pupils' behaviour and well-being.
Of the recommendation to scrap science Sats, the group said it had come to the conclusion that "assessment of the Key Stage 2 science curriculum is not best done through an externally set and marked written test."
Teacher assessment should be used instead, it said.
The recommendations have been accepted in full by Mr Balls.
The expert group's findings are unlikely to appease two of England's biggest teaching unions, the National Union of Teachers and the National Association of Head Teachers, who are to ballot on boycotting next year's tests if they are not scrapped.
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