The board ruled out declaring results of the private candidates on the basis of an alternative assessment policy like that for regular candidates.
But a few are not in favour of the exams getting postponed to July-August or the evaluation system either.
During the hearing conducted through video-conferencing, the apex court observed that the CBSE is likely to take a call on this issue on June 1.
Sisodia, also Delhi's Education Minister, recommended the tabulation of results taking into account the marks students scored in class 10, class 11 and assessment during class 12 so far.
During a high-level meeting called by Ministry of Education to decide the fate of pending class 12 board exams, Delhi Deputy CM Manish Sisodia had put forward the vaccination demand.
The Central Board of Secondary Education (CBSE) has proposed conducting the exams between July 15 and August 26 and the result to be declared in September.
Modi had chaired a meeting on May 21 where the Union Education Ministry briefed him about the extensive consultations done with teachers and parents, and also informed him about the options.
These suggestions were made during a series of sessions on possibilities to conduct class XII board and other entrance examinations this year held by Deputy Chief Minister Manish Sisodia on Saturday.
Exams, internal assessment among likely options as Modi government takes final call on class 12 evaluation
The Ministry of Education has invited suggestions from various stakeholders that will be taken up at the meeting scheduled to be chaired by Union Minister Rajnath Singh.
The board had earlier announced that the entire exercise of tabulation of marks will be completed by June 11 and the result will be declared by June 20.
Compared to CBSE peers, they are at a disadvantage with a 3-month setback; Online format of no help to them.
CBSE officials denied any change in plan 'yet' and reiterated that the arrangements are being made to ensure social distancing by increasing examination centres by over 50 per cent.
Warning that conducting the exams may contribute to the large-scale spread of the virus, he said the centres could emerge as major hotspots.
The fake circular also announced that the dates of results for Classes 12 and 10 exams will be 11 and 13 July respectively. However, the results are tentatively expected on July 15.