The Supreme Court today stayed the admissions on a petition by parents who have challenged the high court's order saying children who have shifted from a different state to Delhi will get no quota.
The court has also issued notice to the Delhi government.
"The admissions already done will be subject to the Supreme Court's decision," said Nidesh Gupta, the lawyer for the parents.
Last week, the high court ended its stay on nursery admissions, ending prolonged uncertainty for thousands of parents.
The court had scrapped the transfer point system after some parents had alleged fake transfers and ordered a fresh draw for the 70 point category.
Nursery admissions have been fraught with chaos for the past few years but this time, the process has dragged the longest, with multiple hold-ups and confusion. Over the last month, the admission process has been stalled at least four times.
Schools have been following a 95-point system to admit children - 70 points for proximity to the school, 20 for a sibling already in the school and five for children of parents who are alumni.