It was reported by RMC Sport on Wednesday that the Frenchman allegedly made comments regarding the number of Black and Muslim players at the Ligue 1 side.
On Friday, Galtier spoke for the first time on said allegations, telling a press conference: "I am deeply shocked by the comments that I am given and that have been relayed by some in an irresponsible manner. And that hurts me in the depths of my humanity.
"I was brought up in a mixed environment and in the values of sharing and respect for others, regardless of their origin, color or background. All my life as a man and as a footballer has been dictated by the concern of sharing and living well with others. I cannot accept that my name and that of my family be sullied in this way.
"I have therefore decided to attack anyone who violates my honor. I have confidence in the justice of my country. And I can only be satisfied with the opening of the investigation.
"The week I spent? It was difficult, very difficult of course. But I took refuge in my work. The moments I was able to spend with the group allowed me to evacuate everything that was said about me".
A further statement was read by a PSG press officer, outlining the club's support of Galtier: "The club supports Christophe Galtier after the unacceptable threats he received and hopes that the truth will be brought by justice.
"Now, the club calls on everyone to take responsibility and to be calm. PSG, its management, its players and all employees, have no tolerance for intolerance on or off the field. The fight against racism is a fundamental commitment of the club and PSG will not be troubled by this episode. And everyone remains fully focused on tomorrow's game".
The situation has developed since an email sent by former Nice Director of Football, Julien Fournier, to the INEOS director Dave Brailsford was leaked.
The email detailed several situations in 2021 in which Galtier was alleged to have used racist rhetoric and discriminatory comments. It is alleged that Galtier complained that his squad had "too many Black and Muslim players" for the profile of the city of Nice.
Galtier is further accused of failing to allow Muslim players to observe Ramadan and vetoing a player's transfer on the basis of his religion.
Since the allegations became public, the matter has evolved rapidly. Despite Galtier's vehement denials and appeals for immediate legal proceedings, his personal details have been leaked on social media leading to a deluge of messages and forcing him to hire private security.
PSG ultra groups have announced that they are following the situation closely, while adding if any of the allegations against Galtier are proven he should be immediately removed by the club.