The European Roma Rights Centre, based in Hungary, is seeking to overturn a 2000 ruling by the court that although the Roma children suffered from a pattern of bad treatment, it was not proven that the Czech government had "intentionally discriminated" against them.
The centre is bringing the case on behalf of 18 children, and says many countries in central and eastern Europe still discriminate against Roma children by placing them in schools for the mentally disabled regardless of their intellectual capabilities.
Dimitrina Petrova, executive director, said: "Segregation of Roma in separate schools and classes remains a widespread problem throughout Europe."
The children have filed a final appeal, submitting evidence of admissions by the Czech government that disproportionate numbers of Roma were sent to special schools on the "basis of results of psychological tests which were conceived for the majority population and do not take Romany cultural specifics into consideration".
The case points out that Romany people have lived in extreme poverty with little access to formal education for centuries and argues that traditional Western tests for intelligence often misjudge a Roma child's true ability.
There are an estimated 300,000 Roma in the Czech Republic, making them one of the largest minorities. But many claim they suffer systematic persecution and discrimination in society, especially in employment and education.