Prof Smith led a government review of maths teaching
The civil servant in charge of science at England's universities department has apologised for criticising the new Diplomas as "schizophrenic".
Professor Adrian Smith, director general of science and research, had said the government should first aim to get GCSEs and A-levels right.
The Times Educational Supplement said he told a lecture audience there was a lack of joined-up thinking.
He has now told ministers that he "deeply regrets" what he said.
Prof Smith is a former principal of Queen Mary, University of London and led a review into maths teaching for the government.
Speaking at the Commonwealth Club in London, at an event recorded by a Times Educational Supplement (TES) reporter, Prof Smith said: "In core subjects like maths and physics we already have a shortage of qualified teacher cover.
"Are we wise in adding different bits of curricular offerings, each of which will require additional teacher input?
"Are we thinking in a joined-up way when we plan curriculum developments and new programmes, whether we have the teacher power, planning and recruitment?
"Might we not be better getting GCSEs and A-levels right first?"
The BBC's education correspondent, Kim Catcheside, said the new diplomas were the central plank of the government's policy in 14-19 education.
She said Prof Smith was particularly criticising the government's new science diploma, which is supposed to have a more academic focus.
He questioned whether it could offer a challenge to the A-level on the one hand, while offering work-related practical elements on the other.
But his apology was "careful", she said, saying he had not intended to criticise government policy.
The government had to be mindful to the danger of losing such an eminent mathematician as a policy adviser, our correspondent added.
The first Diplomas are being taught already in five employment sectors, though they have struggled to attract learners.
The intention is to have 14 of these more vocational "lines of learning", as they are known, in place by 2013.
There will also be three "academic Diplomas" in the humanities, languages and science.
Prof Smith said the science diploma was a "slightly schizophrenic" concept because of its twin challenges, the TES reported.
He was taken to task in some quarters for using the term inaccurately and pejoratively, in light of the current anti-stigma campaign on mental illness.
The civil servant also said: "If you ask a lot of scientists, chemists and engineers what turned them on in the first place, I am afraid it was things like making bombs.
"I think both in terms of funding, in terms of qualified teachers, and the insidious effects of health and safety legislation, we may have done something rather damaging to that fundamental curiosity.
"We need more explosions in schools."
A spokeswoman for the Department for Innovation, Universities and Skills said Prof Smith had written to both education secretaries of state apologising for his remarks.
She said he now "deeply regrets" what he had said and was sorry for causing any embarrassment to the government.
"Since making these comments Professor Smith has made it clear to ministers that he regrets they could be seen to undermine the important work under way to improve the take-up of Stem subjects (science, technology, engineering and maths) across government and the education sector."
She added: "His comments were made as part of a wide-ranging and open discussion and were never meant as a criticism of government policy.
"Professor Smith took up his government post late last year and his remarks do not reflect the advice he has given to the secretary of state."