Kumar told the apex court that it is impossible to re-conduct the exam within the time frame decided by the Supreme Court.
He said that the board (CBSE) was overburdened with work of conducting seven exams simultaneously and it needed at least three months time to conduct the exam afresh.
The Supreme Court had on June 15 scrapped the AIPMT-2015 and had ordered re-conduct of the examination within four weeks.
The apex court had directed the re-examination in view of large-scale cheating in the test with students getting answers in the examination hall at many places.
Earlier, while reserving its order on June 12, the court had said the examination stands vitiated even if one student is being benefited illegally.
It had said that CBSE could not be held guilty as such but taking into consideration the past incidents, "CBSE ought to have been cognisant of these things".
CBSE, however, had opposed the contentions seeking cancellation of the test, saying, "6.3 lakh students cannot be made to take the exam afresh when only 44 students have been found involved in taking benefits through unfair means."
Earlier, the vacation bench had asked Haryana Police to file a fresh report indicating the number of beneficiaries of the alleged irregularities in the pre-medical examination.
It had also asked police to identify as many candidates as possible who had been benefited from the alleged leak.
CBSE was to declare the results of AIPMT, taken by over six lakh students, on June 5 but it was stayed by the Supreme Court.
The court had said, "The bigger issue is that the sanctity of the examination is under suspicion. We want to be doubly sure that there is no alternative but to order re-conduct of the exam," adding that it did not want to take a decision "in haste".