Arkansas' Democratic Governor Mike Beebe has vetoed a bill to ban most abortions in the US state at 20 weeks into pregnancy.
However, politicians can override his decision with a simple majority vote.
The measure would provide exceptions only in cases of rape, incest or to save a mother's life.
It had been approved by an 80 to ten vote in the state House and by a 25 to seven vote in the state Senate.
It is one of several bills introduced by Republicans this year seeking to restrict abortion.
Arkansas currently limits abortions after 25 weeks.
Mr Beebe said in his veto letter that because it "would impose a ban on a woman's right to choose an elective, non-therapeutic abortion before viability, (the bill), if it became law, would squarely contradict Supreme Court precedent".
Veto overrides have been historically rare in the state.
Political science professor at the University of Arkansas Janine Parry said: "In this case, however, an override may be likely, not only because it's easily done but because the partisan dynamics are so dramatically changed".
The Family Council of Arkansas, which supports the bill, started an online campaign yesterday to override Mr Beebe.
"A strong majority of Arkansans are pro-life," the council said on its website.
The bill does not include an exemption for any lethal fetal disorders. Abortion rights activists have said that restrictions on access to safe abortions would be bad for Arkansas women.
"This veto sends a message to the Arkansas Legislature that lawmakers need to quit focusing on unconstitutional abortion bans that are dangerous for Arkansas women," said Jill June, president and chief executive of Planned Parenthood of the Heartland.
Seven US states have laws that restrict or ban abortion after the 20-week mark, and similar laws approved in Arizona and Georgia are facing legal challenges.
Late-term abortions remain relatively rare.
Most of the recent state laws banning most abortions after 20 weeks are based on hotly-debated medical research suggesting that a fetus feels pain starting at 20 weeks of gestation.
Arkansas lawmakers also are considering banning most abortions at about 12 weeks of pregnancy, once a fetal heartbeat can be detected by a standard ultrasound.
State representatives voted 68 to 20 to approve the "heartbeat" bill, which provides an exemption for highly lethal fetal disorders.
State senators approved such a bill in January but must vote again on the current version.
Opponents of that bill say it would be the most stringent restriction on abortion in the country if it became law.