Nicki & Mariah Feud

Nigel Lythgoe tells TMZ, "The statement [that Nicki made a death threat] is absolute rubbish. It's absolutely not true in any way, shape or form." Nigel adds that Mariah confronted Nicki this morning and asked if she made the death threat and Nicki said absolutely not. Nigel says Mariah's people are stirring the pot and gave her bad info.

Nicki Minaj's rant on the "American Idol" set Tuesday went way beyond name-calling ... she threatened Mariah Carey's life -- this according to sources connected to the production.

Our sources say ... in the heat of the argument, Nicki said, "If I had a gun I would shoot her."

The alleged threat was not captured on the video obtained by TMZ. But this is interesting ... if you listen to the audio closely, 11 seconds in you hear Nicki say to Mariah, "Off with your head! Off with your head!."

There's a reason Ryan Seacrest is so rich ... he KNOWS conflict makes shows successful -- claiming yesterday's Nicki Minaj-Mariah Carey blowout is a good thing ... for "American Idol" ratings.

Seacrest just took to his radio show, addressing the TMZ video in which Nicki goes off on Mariah during an audition Tuesday. Ryan said, "We want that!"

"We want them to be on this panel together. This is a good team, a great team, to go out and look for the next American Idol."

Seacrest said, "[There's] nothing wrong with disagreeing ... That's gonna happen, and it's okay."

He added, "These are all very different individuals with different perspectives and different opinions that provide for interesting conversation and dialogue and feedback for the contestants."

9:47 AM PT -- Sources tell TMZ, Nicki's rant on the "American Idol" set went beyond mere name-calling Tuesday ... the rapper also threatened Mariah's life, saying, "If I had a gun, I would shoot her."

Nicki Minaj derailed the "American Idol" auditions in Charlotte, North Carolina Tuesday, after swearing at Mariah Carey and threatening, "I'm gonna knock you out" ... but Mariah FIRED RIGHT BACK with insults of her own.

In the footage, obtained by TMZ, Nicki is clearly furious ... shouting, "I told them I'm not f*ckin' putting up with her f**kin' highness over there."

Mariah can be heard saying, "“Oh why, WHYYYY .do I have a three year old sitting around me?”

Carey continues, "I can’t see my kids, because you decided to act like a little crazy bitch and go all around the stage.”

Sources say Nicki later threatened to "knock out" Mariah ... but she said it before the video starts.

It all went down while the two were sitting at the judge's table ... with Keith Urban sitting in between them and Randy Jackson sitting on the far end, next to Mariah.

We're told the whole thing exploded over a disagreement over a contestant's performance.

Listen closely as you play the video ... you'll hear

Nicki: Think I'm playin? Think this sh*t is a f*cking joke? Think it’s a joke? Think it’s a joke? Think it’s a joke? Say one more disrespectful thing to me, if you say one more disrespectful thing to me -- off with your head!

Mariah: I am not being disrespectful.

Nicki: Off with your head, off with your head.

Nicki: Don’t tell me I'm insecure, don’t tell me I'm inadequate ... you gonna get sent [inaudible] just fall back; don’t ... you don’t know [inaudible] I don’t feel inadequate. You’re the insecure one sittin' up there running down her resume every five minutes.

Nicki: Every time you take a shot at me I'ma take it back, and if you gotta f*cking problem then handle it. I told them, I'm not f*cking putting up with your f*cking highness over there ... figure it the f*ck out. Figure it out.

Mariah: whyyyy, whhyyyyy ...

Nicki: Figure it out

Mariah: ... do I have a 3-year-old sitting around me???

Nicki: I’m not sitting here for 20 minutes and having you run down your resume everyday, No! Goodbye!

Mariah: Listen ... I can’t see my kids because you decided to make ... to have ... to have a little baby fit and going all around the stage.

Nicki: Good, well then go see them now, go see them now ... you’re boring as f*ck, you’re boring as f*ck.

According to our friends at MouthToEars.com, producers ended the auditions for the day so the two judges could cool down. We've confirmed that happened.

Big wigs on the show seem uncharacteristically upset by the blow up. It seems producers are worried about Mariah and Nicki co-existing for the long haul.

Mariah Carey pulled Nicki Minaj aside yesterday and convinced her ... feuding would not be good for the show, and they both needed to stop the antics they pulled during Sunday's auditions.

"American Idol" sources tell TMZ ... Mariah and others were ticked off Sunday that Nicki arrived 45 minutes late ... and that set the tone for the whole day. Although Nigel Lythgoe is saying everything was hunky dory Sunday, we know it wasn't. Mariah talked over Nicki, criticizing her critiques, and Nicki fired right back.

Mariah Carey wasted no time proving what we told you 2 weeks ago -- there's only room for one diva on "American Idol."

Carey and Nicki Minaj went at it during the first "A.I." taping Sunday in NYC. When Nicki started critiquing a contestant, Mariah would interrupt -- not once, but many times. Each time Mariah interrupted, Nicki fought back by loudly talking over Mariah.

One "A.I." spy said Mariah and Nicki tried to cover their disdain for each other but everyone saw through it, adding, "These girls just don't like each other."

You may recall, we reported when producers called Mariah to tell her that Nicki would probably be joining her as a judge, she hung up the phone.

Mariah Carey doesn't need no stinkin' co-judges on "American Idol" ... the diva tells TMZ she can do it all by her damn self!!!! And with multiple personalities, she's just the person to pull it off.

Carey spoke to photogs on both ends of the country yesterday -- first in NYC, where the paps asked about the tension between herself and Nicki Minaj.

Carey shot back, "What tension? There's no tension!" Suuuuure.

When she arrived to L.A. we asked Carey who she would like to join her on the judge's panel, since there are still 3 open chairs.

Mariah replied, "I'd answer that, but I'm not quite sure how."

When we suggested she judge the show by herself, Carey made it clear she LOVED that idea ... saying, "Naturally ... why not?"

Mariah Carey: "Hello, who's calling Mariah?"
American Idol: Hi, Ms. Carey! Sorry to bother you, but we umm ... well, we want the much younger Nicki Minaj to sit next to you at the judges' tab--((dial tone)) Hello? Hello??

Nicki Minaj may well become a judge on "American Idol," but it will be at the expense of Mariah Carey, who we're told hung up the phone when she was told Nicki was the top candidate.

Sources connected with "Idol" tell TMZ ... Mariah was led to believe she would be the only woman on the judge's panel. Choosing Nicki would not only crush that expectation, it would add insult to injury because Nicki (29) is a lot younger than Mariah (42).

As for the composition of the judge's panel, we're told by no means is it a done deal. There are 2 scenarios being played out. First, it's unclear if Randy Jackson will come back as a judge or a mentor. If he leaves the judge's panel, there will be another spot to fill.

The second scenario ... we're told some of the honchos believe it's a mistake to have 2 women and a man on the panel, and a 4th male judge would be necessary.

As for who's still in the running, we're told Brad Paisley, Keith Urban and Enrique Iglesias are leading the pack.