"The bill is so ambiguous and so vague that doctors cannot be certain what medical circumstances would be considered 'necessary to preserve the life of the mother,'" Governor Mary Fallin yesterday said in a statement that labeled the measure "unconstitutional."
"The absence of any definition, analysis or medical standard renders this exception vague, indefinite and vulnerable to subjective interpretation and application," she added.
Fallin, who is known for her anti-abortion views, has been mentioned as a potential running mate to Donald Trump, the presumptive Republican presidential nominee.
The measure, which was sure to face legal challenges, was introduced by Republican Senator Nathan Dahm, who has said he hoped it would lead to overturning Roe v. Wade, the 1973 Supreme Court decision that legalized abortion in the United States.
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In Washington, Senate Republicans have blocked efforts by US President Barack Obama to replace conservative justice Antonin Scalia, who died in February.
Abortion remains a hot-button issue in America and a number of states have moved in recent years to enact abortion restrictions that have led to the closure of many clinics.