Gavin Williamson has "done his best in very difficult circumstances", the health secretary has told the BBC.
Matt Hancock defended the education secretary amid ongoing criticism over A-level grading in England.
The government was forced into a u-turn on Monday after an algorithm to moderate teacher-assessed results led to lower grades for thousands.
Mr Hancock said the government was facing "massive unprecedented operational challenges".
The decision to allow students to use the grades estimated by their teachers - or stick to the grades provided by the algorithm if they were higher - followed similar decisions in Scotland, Northern Ireland and Wales.
It will also apply to GCSE results, which are due to be published on Thursday.
Prime Minister Boris Johnson, who is currently on holiday in Scotland, held crisis talks with Mr Williamson and senior officials on Monday to discuss the change in policy.
Labour has now claimed the algorithm - which saw 40% of A level results downgraded - was "unlawful", saying both Mr Williamson and regulator Ofqual would have "been fully in the knowledge" it breached rules when it was agreed.
A head teacher's union, the Association of School and College Leaders (ASCL), has written to Mr Williamson calling for a review into the "flawed" original plan, saying "public confidence has been badly shaken".
After announcing the change on Monday, Mr Williamson told the BBC he was "incredibly sorry for the distress" caused to students, but he repeatedly refused to say if he would resign.
He has been accused by Labour and the Lib Dems of trying to shift the blame for the debacle on to regulator Ofqual.
The Tory chairman of the education committee, Robert Halfon, has called for Ofqual to be abolished so that ministers can have "proper control and accountability".
But on Wednesday, the Department for Education (DfE) gave the organisation its backing.
A spokesman said: "We have full confidence in Ofqual and its leadership in their role as independent regulator and we continue to work closely with Ofqual to deliver fair results for our young people at this unprecedented time."
The statement also said the decision to change to teacher-assessed grades was taken by the regulator, and the department "agreed" with it - despite Mr Williamson telling the BBC on Monday he "made the recommendation".
A source close to the education secretary suggested to the BBC Mr Williamson did not claim to have made the decision - which rested with Ofqual - but made the recommendation to the government.
But Liberal Democrat education spokeswoman, and leadership contender, Layla Moran said Mr Williamson had "claimed credit for the U-turn while throwing the regulator under the bus".
She reiterated her call for the education secretary to step down, tweeting: "If he has been dishonest as well as incompetent, surely the PM must accept his resignation."
A DfE spokesman said: "Our focus remains on working with Ofqual to ensure students receive their final GCSE, AS level and A-level results this week so that they can move on to the next stage of their lives."
After reports Mr Williamson had tendered his resignation, Mr Hancock was asked whether he would have stood down.
The health secretary told BBC Radio 4's Today programme: "All of us are dealing with unprecedented challenges and unprecedented circumstances. There has never been a year when we haven't been able to do the exams.
"Gavin has faced these very difficult challenges and done his best in very difficult circumstances.
"The huge focus now is on making sure they can get to university in only a few weeks time and also that the schools reopen in a fortnight."
How did Gavin Williamson survive the exams U-turn?
The career aspirations of many teenagers were delivered a blow last week. So why are the career prospects of Gavin Williamson not in tatters?
It's not just some students, teachers and parents who are scratching their heads over this question - but some Conservative MPs too.
One of them said to me: "Any minister who makes children cry is not in a good place."
Another pointed out that he had plenty of time to prepare for how students should be assessed - exams were cancelled five months ago, on 18 March.
Yet Downing Street maintains the prime minister has full confidence in Gavin Williamson.
However, Mr Williamson is still facing pressure from opposition parties, parts of the education sector and students to step down - as well as from some unnamed Tory backbenchers and normally supportive newspapers, such as the Daily Mail.
Conservative former minister George Freeman said the "exam shambles" raised "worrying" questions about leadership at the Department for Education.
Fellow Tory ex-minister and former MP Sir Nicholas Soames tweeted on Monday: "What could have been in the prime minister's mind that led him to appoint so mere, so unreliable, so wholly unsuitable a man to one of the most important jobs in government?
"A catastrophic misjudgement, Williamson must go."
In his letter to Mr Williams, general secretary of the ASCL, Geoff Barton, said: "It seems to be clear that the statistical model for moderating centre-assessed grades was flawed and that it produced many anomalous results.
"But how did this happen, why were the problems not foreseen, and why were ministers not on top of this?"
No 10 has said the prime minister has full confidence in the education secretary.