The Susan B. Anthony (SBA) List tied the District's policy to the grisly murder trial of Kermit Gosnell, an abortion doctor accused of killing several infants in Philadelphia.
"Congress must act immediately to protect children from the Gosnells of our nation," SBA List President Marjorie Dannenfelser said in a statement.
"It is an outrage that in the shadow of the Capitol, children can legally have their lives ended through methods equally brutal to those employed by Gosnell," she said.
Franks's bill would prohibit abortions in the District of Columbia after 20 weeks' gestation, based on the disputed premise that fetuses can feel pain at that stage.
It will be opposed by supporters of abortion rights and the D.C. "home rule" movement, which believes Congress should not set policy in the District.
In a statement last week, Del. Eleanor Holmes Norton (D-D.C.) vowed to defeat the Franks bill on behalf of District women.
"We will combat the insatiable Republican obsession with interfering with the rights of women in our city, as we have successfully done before," she said.