Nicki Minaj and Mariah Carey American Idol Fight Caught On Video

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."

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 Get this s**t in self control. Get in control. Get in control.
Randy Settle down, settle down
Nicki Don't lose your head. Don't lose your head (inaudible). Don't tell me I'm a gangster.
Nicki (inaudible) every 5 minutes. So every time you patronize me, I'm-ma take it back, and if you've got a f**king problem, handle it.
Nicki I told them I'm not f**kin' putting up with her f**king highness over there. Figure it the f**k out. Figure it out.
Nicki I'm not gonna sit here every f**king minute to have you come down and harass me every minute everyday.

Mariah is talking back at Nicki but it's hard to hear what she's saying.

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.