The actors filmed a passionate love scene in response to enduring speculation about the relationship between the eponymous FBI director and his protege Clyde Tolson.
"They ate lunch and dinner together every day, went on vacations together," DiCaprio explained to The Mirror. "Whether they were together in any other respect - well, no-one living knows the truth. In the film, it's seen as almost an unrequited love, but a lasting one, nonetheless.
"These [kisses] are the things we do as actors - I was in character. Clint was very clear, saying, 'I want you guys to beat each other up first, I want as much blood as possible, and I want you to grab each other as if you want to kill each other – and then it will happen'.
"He was very adamant about the fact these men were of a certain time period and no matter what they felt it wasn't something they wanted to express. There was so much bottled up with their emotions for one another, it resulted in two men going fisticuffs first."
DiCaprio also described J. Edgar as one of the "most challenging characters" he has ever portrayed, adding: "It was terrific to breathe life into this person, because he was such a mystery... From a character aspect, he was just a great grab bag of different eccentricities. You name it, this guy had it.
"We tried to give hints - from his obsession with cleanliness, to his stuttering, issues with his mother, questionable sexuality, the repressed lifestyle, obsession with communism and ambition for personal glory."
In the same interview, DiCaprio admitted that he would like to win an Oscar for J. Edgar.
The film is playing in US cinemas now and is released in the UK on Friday (January 20).
Watch a trailer for J. Edgar below: