Jake Paul, Julio Cesar Chavez Sr. Go At It During Fight Press Conference

Verbal jabs were thrown during the Jake Paul vs Julio César Chávez Jr. press conference ... but it wasn't between the two combatants -- but rather Paul and and his opponent's dad.

The two jawed at each other after event moderator Chris Mannix asked the 62-year-old how he believes the bout will go down between his son and El Gallo.

"He's never faced a fighter like my son," the boxing great said. "With all due respect, fighting Mike Tyson, I think I would have given him a better fight. He didn't throw one punch all fight."

"This time, he's gonna get f***ed up."

Paul didn't hold back against the father-son duo ... promising them the fight will end with him turning Chávez Jr. "into another meme with your head in your hands and another disappointment in your son."

Of course, the two have a language barrier ... so Chávez Sr. asked for clarification on what he said -- and Paul broke it down into simpler terms.

"F***ing puta," Paul clapped back. "That's what I said, f***ing puta."

Outside of that, it was a tame press conference between the two sides ... and we take it they're saving the best for when they take the ring on June 28.

Most Valuable Promotions also had some big news on Wednesday -- the promotion announced it signed former UFC bantamweight champion Holly Holm ... and she will be fighting the undefeated Yolanda Vega on the event's undercard.

"This new chapter is going to be an exciting journey, and I'm looking forward to the challenge," she said in a press release.

"With boxing titles in three higher weight classes under my belt, I'm eager to pursue a fourth title in a new division."