The FBI has demoted two veteran agents who were tasked with investigating threats made against Stephen Miller's wife ... and a new bombshell report claims it was done following an argument over the legitimacy of the inquiry.

The FBI confirmed to MSNOW that Special Agent in Charge of counterterrorism, Michael Burgwald, and Assistant Special Agent in Charge, Courtland Rae, were the ones demoted.

The Washington field office counterintelligence agents apparently clashed with FBI director Kash Patel more than once in the past ... but investigating whether or not threats against Katie Miller were terroristic in nature was the straw that broke the camel's back ... this according to MSNOW.

Burgwald and Rae pushed back ... and then they were demoted.

But not so fast, according to the feds ... Washington field office's assistant director in charge Darren Cox denied that the reassignment order came from Kash.

Darren told MSNOW their demotions were a "personnel decision made at the Washington field office level alone based on our constant evaluation of mission needs."

The two agents have since been transferred back to headquarters ... according to MSNOW.