The pair were in LA to exchange words ahead of the fight on 25 August in Manchester.
“This is what you’re going to say once you lose,” he said. “I’ve made a severe and continuous lack of my judgement.”
The comment is in reference to a video uploaded by Logan in January, in which the vlogger apologised for showing footage of an apparent suicide victim whilst in Japan.
The YouTuber then walked over to KSI and proceeded to take off the fake wig before reaching for his bandana.
KSI then made a lunge for Logan before teams from both sides stepped in.
Answering a question about how he felt ahead of the match, Deji said: “My state of mind right now is just to kill you. I want to end you. I’m going to end you.”
Meanwhile, Jake said: “I don’t know if this kid is joking or not.
“Who’s seen his boxing videos? Walmart!”
The press conference also saw Jake hand Deji a bra, ahead of the pair facing off against each other.
The gifting of presents continued into Logan and KSI’s event, with the latter giving the American a pair of Toy Story alien plushies and a copy of YouTube for Dummies.
The Pauls retaliated by stamping of a poster of KSI and handing out toilet rolls with his face on.
During their question and answer session, KSI said: “It feels good to be in LA. How shall I start this? One thing: fuck the Pauls!”
Elsewhere, when host Shannon Briggs, a two-time boxing champion, referred to KSI as “the champ”, Logan replied: “‘The champ’? There’s an asterisk there: ‘The champ for a limited time only’.”
Tickets for the boxing match go on sale on Friday 22 June at 6pm (GMT) and can be bought online.
The full livestream can be found on both Logan Paul and KSI’s channels on YouTube.