Schools Secretary Ed Balls has told MPs delays to the marking of this year's national tests are "unacceptable" and "lessons must be learned".
Thousands of children in England are still waiting for the results of Sats tests in English, maths and science.
The results should have been published more than a week ago by ETS, the US company contracted to deliver them.
Mr Balls declined to apologise for the problems, saying it was the job of the exams watchdog to manage the process.
He was responding to tough questions from MPs on the Commons children, schools and families committee.
He had been due to appear before them to review the annual report for his department but the session was dominated by what MPs have called the "shambles" of the marking of national tests taken by 11 and 14-year-olds in May.
Mr Balls said he, like many parents, heads and teachers, had been upset by the delays.
"It's unacceptable what has happened and we need to learn lessons from that," he said.
Quality of marking
The MPs raised questions about the awarding of the contract to ETS - worth £165m over five years - and about the quality of the marking.
Committee chairman Barry Sheerman MP said he had information that the company was using as markers some people who had only A-level education rather than a degree.
He said he had raised the issue yesterday at a meeting with Kathleen Tattersall, the head of Ofqual, the new body charged with monitoring standards in the exam system.
"They were astonished when I produced a piece of evidence which I know to be true," he told Mr Balls.
"An agency hired a graduate to mark science, maths and English papers. He was the most experienced member of the team."
Mr Balls said he had been assured by Ofqual that the quality of marking was not in question.
The schools secretary was asked if he would say sorry or accept responsibility for the problems.
Mr Balls said ultimate responsibility did rest with ministers, but that the testing regime was run on the government's behalf - at arm's length - by the Qualification and Curriculum Authority (QCA), which contracted out the process of marking the tests to ETS.
"Ministers are accountable to Parliament for the overall delivery of schools policy, including the national testing regime. It is my responsibility to make sure that happens and we do that in an arms-length way."
"We've all had a very bad experience with this and I apologise to teachers and to ministers and others for the performance of the contractor"
Earlier, Ken Boston, the chief executive of the QCA, told the BBC Today programme he was "very bitterly disappointed" at what had been a "very serious failure".
"We've all had a very bad experience with this and I apologise to teachers and to ministers and others for the performance of the contractor," he said.
"This is a very poor situation and we are now in a position where we have to recover it and rebuild it for next year."
His comments followed revelations that some exam papers taken by 11-year-olds remained unmarked 24 hours after he had assured MPs that all had been marked.
Boxes of unmarked papers had been sent back to a school in Lancashire.
"Quite frankly, I am very bitterly disappointed to find that yesterday, having made that remark, another 384 scripts came to light at key stage 2," Dr Boston said.
Results from tests taken by 11-year-olds in English, maths and science should have been published online on July 8, but the release was delayed after problems emerged in the administration of the test marking.
FROM THE TODAY PROGRAMME
Dr Boston told an emergency meeting of the Commons children, schools and families committee on Monday that the QCA was "exploring all possible commercial and legal avenues to ensure that suitable action for this failure is taken".
Asked on the Today programme if he considered ETS incompetent, he said: "On this basis they have not delivered."
MPs at Wednesday's committee meeting pressed Mr Balls over the awarding of the contract.
He said that was a legally sensitive area but one which would be considered in detail by the inquiry he had set up to look into the Sats problems, led by Lord Sutherland.
The remit for Lord Sutherland's inquiry have been published by Ofqual. It will include:
The inquiry will also look at matters concerning responsibilities of the Department for Children Schools and Families (DCSF).
Shadow Children’s Secretary Michael Gove said: "Ed Balls says ministers are responsible for national testing but he refuses to apologise to the thousands of children, parents and teachers who have been hurt by this year’s marking fiasco.
"Ministers urgently need to demonstrate proper accountability by answering the questions about how they ignored the warnings and allowed this fiasco to take place."
Liberal Democrat spokesman David Laws said: "Ed Balls must stop ducking his department’s responsibility for this year’s shambolic marking of national tests.
"It is unbelievable that tens of thousands of pupils are going to have to wait until the autumn before getting the results of what are supposed to be critically important tests."
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