Exam boards that run IGCSEs plan to offer them, while many other exams have been stopped by the pandemic.
IGCSE qualifications, alternative exams to GCSEs, are not usually available in state schools.
Pupils in England whose A-levels and GCSEs are cancelled will depend on replacement grades from teachers.
But Education Secretary Gavin Williamson's scrapping of exams this summer does not apply to students taking IGCSEs.
A Department for Education report in 2019 found 94% of IGCSEs were taken in private schools, accounting for 164,000 exam entries.
The decision not to cancel them was welcomed by the Headmasters' and Headmistresses' Conference (HMC), representing some of the most prestigious independent schools.
The HMC's general secretary, Simon Hyde, said their schools "would be the first to cheer if pupils educated by the state had the same opportunity".
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"The decision to cancel GCSEs was premature. Exams are the fairest way of assessing what learners know and understand and we would like to see as many pupils as possible take a form of exam in the summer," said Dr Hyde.
Independent schools often offer a mix of IGCSEs and GCSEs for different subjects, although IGCSEs do not count towards school league tables.
The qualifications - International GCSEs - are offered by Cambridge Assessment and Pearson and are taken in other countries as well as the UK. Both boards say they are planning to go ahead with exam papers for UK schools this summer.
IGCSEs were not included in the cancellation of exams announced by England's Department for Education and it will be up to individual schools to decide whether to continue with them.
Julie McCullloch of the ASCL head teachers' union said: "It creates another inconsistency, but none of this is easy."
She said it created an "odd situation" when GCSEs were cancelled but IGCSEs were going ahead, but she recognised that an international qualification could need a common approach across different countries.
With the latest lockdown and most pupils studying at home, GCSEs and A-levels have been cancelled in England, Wales and Northern Ireland.
In England, the exams watchdog Ofqual will launch a consultation next week on a replacement way of deciding grades - but Ofqual does not regulate IGCSEs and they will not be part of the watchdog's proposals.