Controversial alternatives to GCSEs have been criticised for not compelling pupils to study Shakespeare and for allowing them to use calculators in maths exams.
International GCSEs, which are being taken up by increasing numbers of private schools, have been accused of falling short of traditional GCSEs in English and maths.
Ed Balls, the Schools Secretary, said people would be "very concerned" if state schools did not require the study of Shakespeare and offered calculator-only maths.
"I think the very people who support the IGCSE in English would be appalled if I were to support a qualification that did not support the study of Shakespeare at 16," he said.
His comments follow the decision by the independent Manchester Grammar to abandon GCSEs in favour of the international qualifications, which its head, Christopher Ray, claims will be better at stretching the brightest pupils.
The IGCSE has soared in popularity in recent years, with 46 per cent of private schools offering at least one of the courses this year - up from 34 per cent last year.
But Mr Balls and John Dunford, general secretary of the Association of School and College Leaders, said this week that some private schools were adopting the qualifications as a "marketing tool" to make them stand out, not because they were tougher.
"The idea that the only schools truly stretching pupils are those private schools teaching IGCSEs is nonsense," Mr Balls said. "It makes a mockery, and ignores the reality, of the great strides in attainment in recent years across the board."
Cambridge Assessment, the board that offers the international qualifications, defended the syllabuses, saying Shakespeare was on the curriculum if schools chose to include it and there were alternative maths courses to choose from, some of which had non-calculator exams.
Claims that the main foreign language exams did not require pupils to take an oral test were wide of the mark, a spokeswoman added.
Dr Dunford, speaking at the ASCL's annual conference in Birmingham, said the trend towards the international qualification was creating an "unfortunate split" between state and private schools that made it hard to compare pupils "like with like".
He criticised Martin Stephen, head of the Pounds 16,500-a-year St Paul's School in west London, for making "insulting" comments about GCSEs.
Dr Stephen, whose school offers IGCSEs in science, maths and music, has described some GCSEs as "appalling" for the most able pupils. "They are baby food - they are examination rusks in too many subjects," he said.
The row over IGCSEs comes amid fresh criticism of changes to science GCSEs, which allow pupils multiple re-sits. In some versions, only the best scores are counted towards pupils' final grades.
The IGCSE has been approved by Ofqual, but has yet to win government approval; without it, state schools will not receive funding to teach them and the results will not be recognised in league tables. A decision from ministers is pending.
Bexley Grammar in Kent was the first state school to ask permission to run the IGCSE in science, but it was turned down.
Rise of the IGCSE
International GCSEs were developed by the Cambridge Assessment exam board in the 1980s and are now used in more than 100 countries.
They offer a more traditional structure than regular GCSEs, focusing on final exams rather than coursework or modules.
Their widespread use in other countries means IGCSEs do not follow the national curriculum.
In 2006, the Qualifications and Curriculum Authority said the IGCSE was not suitable for assessing pupils in England, but it has since been approved by Ofqual, the exams regulator.