"Forty years ago, the Supreme Court affirmed a woman's constitutional right to privacy, including the right to choose," the White House said in a statement.
"This bill is a direct challenge to Roe v. Wade and shows contempt for women's health and rights, the role doctors play in their patients' health care decisions, and the Constitution," the statement said.
The House Judiciary Committee approved the proposed Pain-Capable Unborn Child Protection Act in a party-line 20-12 vote last week. The bill bans abortions 20 weeks after fertilization unless the woman's life is in danger.
That is typically equal to 22 weeks of pregnancy because pregnancies are usually dated from the first day of a woman's last menstrual period.
The House Rules Committee, run by men, added in rape and incest exceptions to the bill Friday and put Rep. Marsha Blackburn, R-Tenn., in charge of managing the House floor debate.
Democrats took issue with the rape and incest exceptions because they make women report the abuse to police if they want to have an abortion. The incest exception is also limited to girls under 18.
The House is expected to vote on the bill Tuesday afternoon.
The bill is widely expected to go no further than the House because of opposition in the Democratic-controlled Senate.
Republican leaders acknowledged to The New York Times the bill's purpose is to satisfy vocal parts of their base that are pushing for greater reproductive-rights restrictions, even if those restrictions hurt the party's reputation with women.