They said that they regret stepping into "a complex political issue", and they didn't intend to offend anyone.
The episode, entitled The Blood of Romeo, aired on June 1. In it, Priyanka's character, FBI agent Alex Parrish, thwarts a terror plot just days before a summit between India and Pakistan is to be held, reports Hollywoodreporter.com.
During her investigations, Parrish finds a religious Hindu symbol - a Rudraksh chain - on the neck of one of the suspects leading her to conclude that the plot was devised by Indian nationalists to frame Pakistan in a nuclear terror attack.
Some fans of the show were upset with the portrayal of Indians in the plot and took to Twitter to express their views. In fact, many fans slammed Priyanka for the track.
ABC Studios clarified that Priyanka had no role in writing or directing the show:
The statement read: "ABC Studios and the executive producers of 'Quantico' would like to extend an apology to our audience who were offended by the most recent episode, 'The Blood of Romeo'. The episode has stirred a lot of emotion, much of which is unfairly aimed at Priyanka Chopra, who didn't create the show, nor does she write or direct it.
"She has no involvement in the casting of the show or the storylines depicted in the series."
They also stressed that "Quantico" is a work of fiction.
"The show has featured antagonists of many different ethnicities and backgrounds, but in this case, we inadvertently and regrettably stepped into a complex political issue. It was certainly not our intention to offend anyone," the statement read further.
"Quantico" will not be getting a fourth season. The third season is on the air in India on Star World.
The cast also included Jake McLaughlin, Johanna Braddy, Russell Tovey, Alan Powell, Marlee Matlin and Blair Underwood.
(With IANS Inputs)