And the intense behaviour didn't let up when time came to actually film his scenes.
Actor Ike Barinholtz, who had a supporting role as Officer Griggs in the film, revealed what it was like to act opposite Leto in a new interview with Howard Stern.
"It was a very fun movie to work on ... He was in character the whole time. At first I was like, 'That's lame.' But then you think about it, and like, I want the Joker to be in character," said Barinholtz.
"I do this scene with Jared Leto and he's supposed to be intimidating me. He comes in, he's the Joker, and he starts squeezing my t*ts. He's like [panting and moaning] 'You're a big guy'."
"This is while we're filming. Then he f**king grabs me and kisses me. On the mouth, full kisses me."
Cameras were rolling and none of this was in the script, mind you.
I thought, OK, I'm just gonna go with it. But then he's like, [panting and moaning again] 'Did someone piss their pants?' I'm like, now I did because you said I did!"
Despite this off-putting behaviour, Barinholtz was full of praise for his famous co-star.
He said Leto was seeking a reaction and "he got it. He was so nice and normal and so cool - I was a fan of his. But then he throws in all this weird sh*t."
While Suicide Squad was a box office hit, it received a critical mauling and left many comic book fans unsatisfied.
In an interview last week to promote rival Marvel franchise Guardians of the Galaxy, that film's star Chris Pratt offered up a theory as to why Suicide Squad underwhelmed.
"One of the flaws might have been they were introducing too many characters in Suicide Squad," he said.
"They spent 10 minutes telling us why should we care about these characters, rather than creating trilogies for each character and convincing us to care about the characters."