The top court said it is the discretion of the Central Board of Secondary Education to conduct the re-examination and can't be challenged in the court.
A bench of Justices SA Bobde and L Nageswara Rao asked the students who had challenged the CBSE's decision to appear in the examination if conducted.
Several petitions were filed before the top court after the CBSE said on March 28 that the Class 10 maths and Class 12 economics paper had allegedly leaked.
The CBSE said yesterday that it has found after assessment there was no impact of alleged paper leak of Class 10 maths paper and no re-examination would be held.
Besides challenging the CBSE's decision, the petitioners also wanted a CBI probe into the alleged paper leak, saying several incidents were reported from various states and Delhi Police was not competent to hold the nation-wide probe.
Besides seeking an independent probe into the leak, one of the petitioners, 15-year-old Rohan Mathew, also sought a direction to the CBSE to declare the results on the basis of the examinations already conducted.
Mathew and two others have moved the top court seeking quashing of the CBSE's decision to re-conduct the Class 10 mathematics examination on several grounds, including violation of their fundamental rights.
Earlier, another plea was filed in the top court by Reepak Kansal, a resident of Shakarpur here, challenging the decision of the CBSE to cancel and re-conduct the two papers.
"It is to be noted that this year, 16,38,428 students are appearing for the Class 10 and 11,86,306 students for Class 12 in the CBSE examinations.
"And therefore, to penalise the student community for an incident which is under investigation and without completion of that investigation/enquiry and issuing a notice on March 28, 2018 (for re-exams), affects the fundamental rights of students which is arbitrary, illegal and unconstitutional," the plea said.