"When will the radical right-wing men in Congress let up?" she said in a statement.
"This can't be said more clearly: Rep. Franks is not the mayor of Washington, D.C., and he has no place taking private medical decisions away from women in the District of Columbia."
The bill takes cues from similar laws passed in six states. District physicians who disobey its terms would be fined or imprisoned for up to two years, and under certain circumstances, it would allow partners and parents of women who have abortions to claim civil remedies.
On Tuesday, Del. Eleanor Holmes Norton (D-D.C.) pressed her Democratic colleagues to oppose the bill.
"There can be no doubt about the national implications of a bill with D.C.’s name on it as a cover for attacking the reproductive rights of the nation’s women," she wrote.
A spokesman for Franks did not immediately respond to a request for comment.
The bill was introduced in January and had 210 co-sponsors on Tuesday. A companion bill from Sen. Mike Lee (R-Utah) was introduced in the Senate in February.