The exam regulator in England says its chair has issued "an expression of regret" over any offence caused by comments about Welsh ministers.
The Welsh government demanded an apology from Ofqual after a claim to MPs that the regrading of GCSEs in Wales was "politically motivated".
Amanda Spielman's words were called "inappropriate" and "ill-judged".
A cross-border government row blew up with the regrading of English papers ordered in Wales but not in England.
On Tuesday, more than 2,300 of the 34,000 pupils in Wales who took the exam received better results after their papers were looked at again.
The Welsh education minister - who is the exam regulator in Wales - had stepped in and ordered a review, which found the original marking criteria disadvantaged students.
However, papers of 84,000 students in England who took the same exam have not been regraded.
An Ofqual spokesperson said: "Following meetings with our regulatory colleagues in Wales this week, we have written to them welcoming the continued joint commitment to three-country regulation, which is best for all students as the qualifications we regulate are relied on by users across the borders.
"The letter also includes an expression of regret from the chair of Ofqual, Amanda Spielman, for any offence caused by comments made at the education select committee hearing."
Ms Spielman had told the Commons committee last week there was "a clear divergence" in performance between English and Welsh candidates which was difficult for the Welsh to accept politically.
In a letter to Ofqual, Chris Tweedale, director of the Welsh government's Schools and Young People Group, had demanded an "unqualified apology from Ofqual's chair by close of play on Friday this week".
The letter also asked Ofqual to retract its claims that it had raised concerns about the standard of "most" of WJEC's GCSE awards.
He said: "This was not the case. GCSE English language (and English) were the only GCSEs about which any concern was raised.
"Given the high proportion of learners in Wales who take WJEC's GCSEs, this is clearly a significant matter for us and I would ask that I receive confirmation that you have issued a correction to these statements by close of play on Friday."
Despite the regrading in Wales, the proportion of those who achieved a grade C for English language was down 3.9% on last year.
Later on Wednesday, the WJEC published statistics showing how the regrade had affected the overall pass rate at A* to C in English language exams across Wales.
In August, the overall pass rate for the English language paper stood at 57.5% - a significant drop on the 2011 figure of 61.6%.
But the regrade pushed the number getting A* to C grade in the subject up to 61.1%. That is still marginally down on last year.
The UK government's Education Secretary Michael Gove was critical of Welsh Education Secretary Leighton Andrews' subsequent decision for directing the WJEC (previously known as Welsh Joint Education Committee) exam board to regrade Welsh students.
On Friday, local authorities, teaching unions and schools began a legal challenge against Ofqual's refusal to re-grade GCSE English papers in England.