The agents believe they were fired on the orders of FBI boss Kash Patel, who is named as a defendant.
Their termination letters accused them of "a lack of impartiality" in their duties, they say. The FBI has declined to comment on the case.
The dozen sacked agents - nine women and three men - say they had been "confronted by a mob" when deployed in the US capital city on 4 June 2020, and were responding to a "dangerous situation" for which they were ill-prepared.