Giving the directive, Justice S Vaidyanathan posted the matter to February 3 for further hearing.
In her petition, the woman sought a direction to exhume Jayalalithaa's body and enable her and her family to cremate it on the grounds that the chief minister was an Iyengar Brahmin. She also prayed the court to order a DNA test.
The apex court, however, had said she was at liberty to approach the high court.
Jayalalithaa died on December 5, 2016 after prolonged hospitalisation and her body was buried off the famous Marina Beach here.
When the matter came up today, Advocate General Vijay Narayan sought time to file the counter affidavit.