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In a clip that circulated online, the 89-year-old, who is the founder and CEO of Top Rank, was surrounded by journalists when he produced a foul-mouthed outburst towards Abdo, who hosted the event ahead of Saturday's trilogy bout.
He believed the presenter was being biased towards the American fighter.
Arum said: "They bring this woman in from the UK and she's slanting all the press conference to Wilder. Like I don't give a damn, but it's obvious what she was doing,"
"And then, she knew that the understanding was: no face-off. Tom Brown argued with Fox, no face-off. We said, 'No face-off'. What does she say? 'Now we're going to do a face-off?'
"F*** her. And f*** them. There was no face-off and we saved the fight."
Several days after Fury retained his heavyweight crown, Bob Arum has now apologised for his actions towards Abdo in an interview with YouTube channel iFL TV.
"As far as Kate is concerned, I was completely wrong," he said.
"We had made a deal with the producer televising the weigh-in and the deal was made on behalf of Top Rank and PBC and the producer agreed no stare-down.
"And when she called for a stare-down, particularly after seeing the animosity, verbally, at that press conference, I exploded but it wasn't her fault.
"The producer reneged and she gets the instructions in her earpiece and she was told to order the stare-down.
"She is a terrific commentator, a terrific reporter and she wasn't the one I should have directed my ire [towards] so I was completely wrong."
After the video of Arum's outburst went viral, Kate Abdo responded with her own statement on Twitter.
"With regards to the face-off, I was doing what we the broadcaster believed we agreed upon, but I think that's kind of unimportant now," she wrote.
"I have nothing but respect for Bob Arum and the empire he has created.
"I understand what he means to boxing and what this sport owes him.
"I think the language in this interview was entirely inappropriate. Of course it's disappointing to be disrespected by someone I respect. But that's life, not everyone will give you the courtesy you deserve."
Thoughts on the incident?
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