Diddy Prosecutors Under Pressure to Get Victim No. 3 to Testify in Court

Federal prosecutors are under pressure relating to one of their star witnesses in the Diddy trial ... because they revealed in court today they may not be bringing an alleged victim into the courtroom to testify.

The alleged victim in question is a woman and the feds revealed Monday the woman does not live close to New York City, where the trial is being held, and they say she's told the court she might not even show up despite being subpoenaed.

Prosecutors claim they are having difficulty contacting the woman and her attorney ... and the judge asked lead prosecutor Maurene Comey if the prosecution planned to drop the woman's name in opening statements.

Comey said the prosecution would not be getting into the woman's story until the second part of the trial ... and during opening statements, the woman would be described as one of the many women who have allegedly been abused and sexually exploited by Diddy.

Diddy's lawyers told the judge prosecutors need to tell them what they plan on doing with Victim No. 3 by the end of this week ... and the judge implored the feds to make every effort to reach the woman's attorney and secure her appearance.

As for Diddy's appearance in court Monday, we're told he covered up his neck tattoo with his sweater and collared shirt ... and none of the prospective jurors made eye contact with him as they came in and out of the courtroom.

Overall, we're told things were mild and copacetic during the first day of trial proceedings ... with prosecutors and Diddy's lead attorney Marc Agnifilo working well together.

Diddy and Agnifilo passed notes back and forth throughout the day ... including one that appeared to be a question Diddy had about one of the jurors who said they did not like to see violent videos.