PALO ALTO, Calif. — A Catholic group is threatening an all-out battle with Miller Brewing Co. after the firm distanced itself from a raunchy San Francisco street fair but apparently did not end its sponsorship of the event.

The Catholic League has expressed outrage over the poster for this year’s fair, which takes place on Sunday. The poster, which evokes a renowned Leonardo da Vinci painting, “The Last Supper,” shows semi-nude men and women in bondage attire seated at a table cluttered with sex toys, whips, and various restraints.

After protests from the Catholic League and another conservative group, Concerned Women for America, Miller said Tuesday that it was asking to have its logo removed from the poster.

“While Miller has supported the Folsom Street Fair for several years, we take exception to the poster the organizing committee developed this year. We understand some individuals may find the imagery offensive,” a Miller spokesman, Julian Green, said in a statement sent by e-mail.

The president of the Catholic League, William Donohue, said his group recently discovered that fair organizers are holding a “Last Supper With the Sisters” event to “prepare your mortal flesh for the kinkiest weekend on Earth.” The gathering is to benefit a group Mr. Donohue called “anti-Catholic and misogynist,” the Sisters of Perpetual Indulgence. The sisters call themselves “queer nuns.”

Mr. Donohue faulted Miller for refusing to cut ties with the fair in light of the “Sisters” connection. “This is an ethical and marketing fiasco of colossal proportions,” he said. “It really is ‘Miller Time.’… Miller has decided to side with a small band of depraved and bigoted gays against Catholics … and Protestants.”

The Catholic activist said he would announce some kind of action against Miller today. “The collision course that Miller wants with Christians is now on,” he said.

Mr. Green did not respond to an e-mail seeking further comment last night.

The nonprofit group that organizes the fair, billed as “the granddaddy of all leather events,” issued a statement Tuesday defending the poster and saying it was not intended “to be particularly pro-religion or anti-religion.”

Asked about the Catholic League’s latest complaints, a spokesman for the fair, Patrick Finger, said, “We have no further comment on this issue.”

As of yesterday, the Miller Light and Miller Genuine Draft logos, are still on the poster on the fair’s Web site. It also lists the beers as “presenting sponsors” of the event, along with two “hardcore” pornography sites, Nakedsword.com and TitanMen.com.