Police said no permission was sought, and that protesters disobeyed instructions and stayed at Akashvani Bhawan.
The Election Commission said the delegation had not sought an appointment and declined its offer to send an officer.
Congress’s Jairam Ramesh called the FIR retaliation.
About 260 people, including 10 MPs, were detained and released before midnight.
The FIR was registered on October 7.
The FIR concerns the alleged unauthorised entry of Congress MPs Rahul Gandhi and Priyanka Gandhi Vadra and other INDIA bloc MPs into the Akashvani Bhawan premises.
ThePrint reported that the other MPs named include K.C. Venugopal, Pawan Khera and Mahua Moitra.
A senior police officer said a case has been registered under relevant sections and that an investigation is under way.
The reports available on October 7 did not specify the sections or the police station.
Police said no permission had been sought for the march from Parliament House to Nirvachan Sadan.
Police said the protesters disobeyed instructions and remained at Akashvani Bhawan, which led to detentions.
About 260 people, including 10 MPs, were detained, according to ThePrint and Asian News International.
The detained leaders were taken to New Police Lines and Kingsway Camp, and all were released before midnight.
ThePrint reported that around 300 opposition MPs led by Rahul Gandhi marched from Parliament House towards the Election Commission office.
The Election Commission said the delegation had not sought an appointment through the established protocol, according to ThePrint.
The commission said it had proposed sending an officer to receive the memorandum, and that the offer was declined, according to the same report.
Congress general secretary Jairam Ramesh described the FIR as retaliation and said the leadership had adopted satyagraha to highlight alleged voter deletions.
The march was held to demand the resignation of Chief Election Commissioner Gyanesh Kumar over alleged irregularities in the Special Intensive Revision of electoral rolls.
Akashvani Bhawan, Parliament Street, New Delhi (file image), Wikimedia Commons, CC BY-SA 4.0
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