Results for Sats tests for 11 and 14-year-olds, due next Tuesday, will now not be delivered to schools until the following week, with some marks not expected to arrive until after the start of the summer holiday.
The National Assessment Agency apologised to schools, pupils and parents for the delay, which it blamed on a "serious failure" by the private firm ETS Europe, which has the contract to carry out marking.
Schools Secretary Ed Balls branded the late delivery of results "completely unacceptable" and announced an independent inquiry, which will report to his Department for Children, Schools and Families and the qualifications regulator Ofqual.
But he said he had been assured there was no question about the quality and accuracy of marking.
Teaching unions said the incident raised questions about the whole system of high-pressure national tests for younger children, which they said was excessive and unnecessary.
The vast majority of the Key Stage 2 Sats in English, maths and science taken in May by 11-year-olds about to leave primary school are now due to be handed out on July 15, with the bulk of Key Stage 3 marks for 14-year-olds in the same subjects expected at the end of that week.
However, it is thought likely that some Key Stage 3 results - particularly for English papers - will not be known until after schools have broken up for the summer.
Reports of difficulties with the marking of the national curriculum tests have been circulating for a number of months, after ETS introduced new arrangements in the first year of its five-year contract.
Teachers reported that they were unable to enter pupils' details on an online database, while markers complained of inadequate training, lost contracts and widespread confusion.
It is understood that some markers decided not to do the job this year, though ETS insists recruitment went well and there was no manpower shortage.
The company blamed technical, logistical and administrative problems, and admitted that some markers were left with no work to do after deliveries of papers failed to arrive on time.
Over the past few weeks, four large panels of markers were set up to work all day and weekends to get through a backlog of papers which had built up.
Mr Balls said today that just 90% of Key Stage 2 marks and levels were ready, while the Key Stage 3 position is "less close to being complete", and the delay was necessary to ensure the "orderly" distribution of results.
In a letter to the chairman of the Commons Schools Committee Barry Sheerman, he said: "The NAA continues to monitor the situation closely and will make its best endeavours to release results to as many schools as possible by the end of term.
"This delay to releasing results to schools is unsatisfactory and will inconvenience schools and headteachers. This is clearly unacceptable."
In a statement, the NAA said that ETS had introduced "a series of additional checks to give greater assurance of high-quality marking" in this year's Sats.
"The main causes of this delay are the lateness in the completion of the marking process and a series of technical issues," said the NAA. "This is a serious failure by ETS Europe for which we apologise to schools, pupils and parents.
"We understand that this delay will inconvenience many schools, and we share their frustration and disappointment."
Ofqual chairwoman Kathleen Tattersall said the regulator had been aware for some time that marking of 9.5 million papers was not progressing smoothly.
She said Ofqual was "disappointed" at the delayed results, adding: "Pupils and teachers work hard throughout the year and it is unacceptable that they have been let down in this way."
An ETS Europe spokesman said the company "regrets the inconvenience" caused by the delays and will co-operate fully with the independent review.
"Our priority is to ensure that all of the tests are marked to a high standard so that schools will receive accurate results to better serve the needs of their pupils," said the spokesman.
"We will report the vast majority of the test results one week late, on July 15, with a small number of Key Stage 3 results to follow as soon as possible."
The Association of School and College Leaders, which represents headteachers, said national exams at age 14 should be downgraded to internal school checks on pupils' progress.
General secretary Dr John Dunford said: "This is further evidence that the high-stakes testing regime in England has become too extensive and unmanageable.
"The important examinations for secondary school students are at 16 and 18 and schools are properly held to account for these results."
Dr Mary Bousted, general secretary of the Association of Teachers and Lecturers, said: "Dealing with 9.5 million papers every year is a massive administrative and logistic undertaking which is prone to shambles and is not worth the money.
"The Government needs to face up to the reality - Sats are beyond their sell-by date."
And Chris Keates, general secretary of the NASUWT teaching union, said: "This key responsibility of the state should not be handed over to private sector profit-making organisations. Taxpayers should ask if this is the best way to spend public money."
Shadow schools secretary Michael Gove said: "I warned Ed Balls about this unfolding debacle in Parliament more than a month ago. Ministers took no action.
"The Government awarded the contract for exams to a company with a record of failure which we exposed. Now at the 11th hour the results have been delayed and question marks hang over their credibility.
"Ministers cannot evade responsibility for the damage done to the credibility of Britain's exam system."
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