Griffin's publicist issued a statement to ABC News that in response to Palin's complaints, the reality star would like to invite the politician to her upcoming Broadway show.
"As a fellow reality star," Griffin's publicist wrote, "Kathy would like to extend free tickets to her upcoming Broadway show to reality-star Sarah Palin and her reality-TV crew. Kathy supports all reality stars regardless of what they say about her."
Griffin, who is gearing up for her Broadway debut in March in a stand-up comedy show dubbed "Kathy Griffin Wants A Tony," which will run from March 11-19.
The comedian has long made fun of Palin, a Republican former governor of Alaska who later starred in her own reality show, "Sarah Palin's Alaska," and her daughter, Bristol Palin, whose teenage pregnancy was a sensitive issue during her mother's 2008 vice presidential campaign and who appeared last year on the ABC series "Dancing With the Stars." Griffin said in December 2010 that she mocks Sarah and Bristol Palin because "it's just fun."
Palin, 47, appeared in a Fox News interview this weekend and said she hoped that Griffin would leave her kids alone.
"You know, Kathy Griffin can do anything to me or say anything about me, because you know, she's kind of this - she's a 50-year-old adult bully is really what she is," Palin said. "She's kind of a has-been comedian and she can do those things to me. I would just ask for respect of my children. ... Kathy, pick on me, come up to Alaska and pick on me, but leave my kids alone."
Griffin has also spoken out about Palin's 16-year-old daughter Willow. The comedian announced that her 2011 New Year's resolution was to bring down Willow, for allegedly posting homophobic slurs on her Facebook page.
The comedian made a crack about Bristol Palin's "Dancing With the Stars" stint in "VH1 Divas: Salute the Troops," which was recorded at the Marine Corps Air Station in December.
"[Bristol is] the only contestant in the history of the show to actually gain weight," Griffin said. "She gained like 30 pounds a week. I swear to God, it was fantastic; she's like the white 'Precious.'"
The comedian also took Bristol's baby daddy, Levi Johnston to the 2009 Teen Choice Awards and visited the Palin's hometown in Alaska to go fishing with Johnston on her Emmy-winning reality series "My Life on the D-List."
Griffin is set to appear in an upcoming episode of "Glee," where she will further upset Palin by playing a character named Tammy Jean, a home-schooling Tea Party candidate who will judge the Regionals competition on the show.