A bench of Justices Sanjiv Khanna and Chander Shekhar asked the poll panel to file the affidavit after the EC said it wanted to respond to some of the allegations made in the lawmakers' pleas challenging their disqualification from the Delhi Assembly.
The Commission also told the court that it would rely upon the opinion it gave to the President to disqualify the 20 AAP lawmakers who were appointed as parliamentary secretaries.
When the matter was taken up for hearing initially, the court asked the petitioners to go through the poll panel's synopsis of the case and then decide if affidavits are needed.
Subsequently, the matter was taken up again after everyone perused the EC's synopsis.
In the second round of proceedings, the bench said that the 250-page long synopsis, containing various documents, was very big and asked the EC to file a shorter one on affidavit.
"A synopsis of 250 pages. It cannot be that big," the court observed.
After the brief proceedings, the court listed the matter for further hearing on February 7 by when the lawmakers have to file their responses to the EC affidavit.
The court also extended till February 7 the interim order restraining the EC from issuing any notification announcing bye-elections to fill the vacancies of the 20 assembly seats whose legislators have been disqualified.
The matter was transferred to a division bench on Monday after Mr Patel moved an application for transfer of the petitions to a division bench.
The high court had on January 24 refused to stay the centre's notification disqualifying the lawmakers, but restrained the EC from taking any "precipitate measures" like announcing dates for by-polls.
It had earlier summoned the entire records pertaining to the proceedings leading to the recommendation of the EC for the disqualification of the 20 legislators which received the President's assent on January 20.
The 20 disqualified MLAs include Adarsh Shastri (Dwarka), Alka Lamba (Chandni Chowk), Anil Bajpai (Gandhi Nagar), Avtar Singh (Kalkaji), Kailash Gahlot (Najafgarh) -- who is also a minister -- Madan Lal (Kasturba Nagar), Manoj Kumar (Kondli), Naresh Yadav (Mehrauli), Nitin Tyagi (Laxmi Nagar), Praveen Kumar (Jangpura).
The others are Rajesh Gupta (Wazirpur), Rajesh Rishi (Janakpuri), Sanjeev Jha (Burari), Sarita Singh (Rohtas Nagar), Som Dutt (Sadar Bazar), Sharad Kumar (Narela), Shiv Charan Goel (Moti Nagar), Sukhbir Singh (Mundka), Vijendar Garg (Rajinder Nagar) and Jarnail Singh (Tilak Nagar).