Gavin Williamson has “done his best in very difficult circumstances”, the health secretary has told BBC News.
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 followed similar decisions in Scotland, Northern Ireland and Wales.
It will also apply to GCSE results, which are due to be published on Thursday.
A head teacher’s union, the Association of School and College Leaders (ASCL), has written to Mr Williams 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.
And 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”.
Asked on BBC Radio 4’s Today programme about reports Mr Williamson had tendered his resignation after Monday’s U-turn, Mr Hancock said: “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.”
And Liberal Democrat education spokeswoman and party leadership contender Layla Moran said: “There must be consequences for this catastrophic failure of governance.
“Gavin Williamson must resign, and if he refuses to go Boris Johnson must sack him.”
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.