Akashvani Bhawan, Parliament Street, New Delhi (file image), Wikimedia Commons, CC BY-SA 4.0
Rahul Gandhi and Priyanka Gandhi Vadra are named, according to the reports.
ThePrint reported that K.C. Venugopal, Pawan Khera and Mahua Moitra are also among those named.
The reports did not specify the sections invoked.
A senior officer said an investigation is under way.
The FIR concerns alleged unauthorised entry.
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.
The reports available on October 7 did not include a response from the Chief Election Commissioner to the allegations.
Akashvani Bhawan, which houses All India Radio, is on Parliament Street and is next to the Election Commission office.
Akashvani Bhawan, Parliament Street, New Delhi (file image), Wikimedia Commons, CC BY-SA 4.0
