Shirley Phelps-Roper of the Westboro Baptist Church in Topeka first told the Topeka Capital-Journal that church members will skip Green's Thursday funeral in Tucson.
Phelps-Roper says the church has been given airtime with 102.1 The Edge in Toronto, Canada, and an interview with KXXT-AM in Phoenix, Ariz. on Saturday morning.
The church's past protests, which have included picketing military funerals, have been highlighted by ardent anti-gay rhetoric - blaming the country's troubles on its acceptance of homosexuality.
Special Section: Tragedy in Tucson
Phelps-Roper says the group still will picket the Friday funeral of U.S. District Judge John Roll and at the intersection where Congresswoman Gabrielle Giffords and others were shot.
In response to Westboro's threat to picket Green's funeral, the Arizona Legislature unanimously passed emergency legislation Tuesday banning protests at or near funeral sites.
The U.S. Supreme Court is currently mulling a case brought by a dead Marine's father who wants to ban Westboro's practice of picketing high-profile funerals - especially those of soldiers - with hateful messages. A decision is expected later this year.
A U.S. flag that flew atop the World Trade Center is to Arizona to be displayed at Green's funeral. She was born on Sept. 11, 2001.
The Arizona Republic reports the 20-by-30-foot flag was the largest to have survived the collapse of the twin towers.
"You know, I've said it before, but the bookends of her life -- she came into the world on a tragedy on 9/11, and she went out on this tragedy [Saturday] in Arizona. But everything in-between has been wonderful, and she's affected a lot of people," John Green, Christina's father, told CBS News Sunday.
"We're just gonna keep on remembering her forever," her mother Roxanna said. "She was a special little girl."
A spokesman for the foundation that displays the flag around the country says it's with a New York firefighter who hopes to arrive Wednesday, depending on the storm in the Northeast.