Pop Idol: Lythgoe warns Cowell, Waterman
The pair's quarrel started when Cowell branded Darius Danesh's performance of "Let's Face The Music and Dance" the worst of the evening.
Waterman responded: "You must have something in your ears, mate, because that was as close as I've ever heard to Nat King Cole in my life."
In the results show later on in the evening, their spat resumed, with Cowell adding: "If you think what I said was about his age, you are talking b******s. If you don't think I'm allowed an opinion, we won't even bother turning up."
Lythgoe, producer of the show, said he has since warned the pair not to repeat such incidents.
"Their argument in last Saturday's show went too far and is unacceptable on any future shows. I reminded them that the talent was appearing in front of them and they should not hijack the show with their own petty quarrels," he said.
"Frankly, I'm disappointed that Simon couldn't take Pete's criticism having dished out so much himself. It looks like he can give it but not take it. The pair of them acted like a slightly senile bickering old couple who had never had enough courage to get divorced 20 years ago."