Jan. 6, 2009  -- The country's largest gay-rights group today demanded an apology from David Letterman, for making what it called "inappropriate and incendiary remarks" regarding President Obama's appointment of a transgender woman to the Commerce Department.

In his monologue Tuesday, Letterman remarked that Amanda Simpson, a transgender woman, had been appointed to work in the Commerce Department's Bureau of Industry and Security, where she will monitor the export of military technology.

As a photograph of Simpson was shown, announcer Alan Kalter shouted, "What? Amanda? Amanda used to be a dude?"

"Oh my God!" he shouted, before running off stage, with audience laughing.

In a letter to Letterman and CBS Entertainment President Nina Tassler, Human Rights Campaign called the bit "inappropriate and incendiary" and said it reflected "transphobia," a fear or hatred of transgender people.

"Your skit affirmed and encouraged a prejudice against transgender Americans that keeps many from finding jobs, housing, and enjoying freedoms you and your writers take for granted every day," HRC's Allyson Robinson wrote in the letter.

Robinson said the punch line of the bit has "been used as a defense in nearly every hate crime perpetrated against transgender people that has come to trial." She cited two cases in which individuals suspected of murdering transgender people claimed they did so in a rage after learning about their victims' gender identity.

Letterman spokesman Tom Keaney told ABCNews.com he would not comment.

Simpson's appointment has drawn criticism from some conservative groups that accuse the Obama administration of pandering to the gay community, a concern she addressed in an interview with ABC News.com on Monday.

"[There will be] questions like: Is this a token? Are you here to do a job or just to fill a quota or appease other people? In that regard it makes it a bit more difficult," she said. "I'm sure I will have to do and intend to do a far superior job than any other person. But I'm sure I will always be second guessed."

Simpson, divorced with a 15-year-old son, began her transition from male to female in 2000.

A former test pilot, Simpson worked in the aerospace and defense industries for 30 years, mostly at Raytheon Missile Systems in Tucson, Ariz. She holds degrees in physics, engineering, and business.

Simpson told ABCNews.com that much of her work will involve "licensing and enforcement for exports" of military technology.

In 2004, she was named by the YWCA as one of their "Women on the Move," and in the same year, she won the Democratic nomination to the Arizona state House of Representatives. She lost in the general election.