The group has been trying to buy a billboard that features Gibson's mug shot with the word "no" over it in red.
They are trying to secure space on the city's famous Sunset Boulevard and have been repeatedly turned down once billboard companies learn the content of the proposed billboard.
Publicist Andy Behrman, who is spearheading the effort, tells website TheScoop.com, "We wanted to make a statement that anti-Semitism is not OK in Hollywood--or anywhere else.
"They tell us it will be fine, and then when they learn we want to protest Mel Gibson, there's suddenly some problem."
Behrman says he even got an OK to erect the billboard on Aug. 15--until ad space bosses learned all about the protest.
He adds, "I got a call back saying, 'My boss doesn't want to touch this Mel Gibson thing.'"
Gibson Invited to Jewish Memorial Museum
Mel Gibson has been invited to visit New York's Museum of Jewish Heritage, a site dedicated to remembering the Holocaust, in a bid to smooth relations between the actor and the Jewish community after his anti-Semitic rant on the weekend.
The star, who launched the tirade at a Los Angeles police officer after being stopped for drunk driving, has since apologized for his strong words.
And his contrite behavior has impressed workers at the memorial museum, who are welcoming him with open arms.
Museum official David Marwell wrote to the star on Wednesday, stating, "I have followed with great interest the events of the past several days and take your recent public apology very seriously.
"In that spirit, I would like to invite you to visit the Museum of Jewish Heritage--A Living Memorial to the Holocaust.
"The message of the museum lies in the two biblical quotes that are carved into our walls and that are part of our shared Judeo-Christian tradition: 'Remember, never forget,' and 'There is hope for your future.'
"We trust that you will not forget what has brought you to this point, but we would also like to support you in your efforts to create a better future."
Gibson, 50, has also been invited to speak to his local Jewish community in Beverley Hills on Yom Kippur, the Jewish Day of Atonement, which falls this year on Oct. 1.
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