An article in Sunday's Scottish press quoted Green using a racial term widely regarded as derogatory, although he claimed it was a "light-hearted" greeting taken out of context.
That explanation has not appeased the Show Racism The Red Card group, whose chief executive Ged Grebby said: "For the CEO of Rangers to use the term in any context is not helpful as it sends out the wrong message to young people.
"The comments of Charles Green are very ill-advised and someone in his public position should really know better than to use this kind of racist and offensive language.
"Show Racism the Red Card has a long standing working relationship with Rangers FC. The club is an excellent supporter of our anti-racism and anti-sectarianism campaigns.
"Show Racism the Red Card work proactively across Scotland educating young people and society about the dangers of racism and sectarianism.
"A significant part of this education is looking into terminology and defining what is appropriate."
Green later accused Show Racism The Red Card of a "knee-jerk reaction", adding: "In the interview, I referred to the fact we are now living in a politically correct world where words and phrases that were once used are no longer acceptable.
"I deplore racism and sectarianism and this football club does a huge amount of work in this area to help eradicate these problems."