The first bench, comprising Chief Justice S K Kaul and Justice M Sathyanarayanan, gave the additional time after after Sagayam's counsel sought eight weeks.
The court also criticized the central government for failing to file its counter-affidavit.
Noting that on August 6, it had imposed Rs 5,000 as cost on the Centre and gave time for a counter, the judges said the filing of the counter within the next three weeks was subject to payment of the costs. If there is any further delay, there would be an additional cost of Rs 10,000, they said.
On November 25, passing orders on a clarification petition by Sagayam, the court had stated that his probe would be confined only to granite mining irregularities in Madurai district and could be further expanded to other districts gradually.
Earlier, Sagayam had filed a petition seeking to know whether he was to probe only granite mining or those relating to river sand and beach sand as well in all 32 districts.
The officer also wanted permission to select his chosen set of officers to assist him in the probe.