MS only has one medical facility that performs abortions in the state, Jackson Women's Health, and the clinic has vowed to fight the new law.
District Judge Carlton Reeves issued a temporary restraining order Tuesday, blocking the law from taking effect for 10 days while the court considers further action.
An AP report said that abortion opponents have sought the legal confrontation, hoping that federal courts will ultimately prohibit abortions before an unborn child is viable.
Republican Gov. Phil Bryant made the comments while he signed the law Monday in a closed ceremony, according to a video his office posted to social media.
The governor was in a jovial mood as he signed the bill into law. The measure is the most restrictive abortion law in the United States.
In a telephone interview late on Monday, Diane Derzis, the owner of the clinic, said that a young woman whose pregnancy was beyond the 15-week limit was scheduled for an abortion on Tuesday.
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He also argued that gestational age emboldens the state's interest in "protecting unborn life". The owner of Mississippi's only abortion clinic opposes the law and has pledged to sue.
The Jackson Women's Health Organization, in a lawsuit handled by the Center of Reproductive Rights, argued the measure is unconstitutional and should immediately be struck down.
Republican legislative leaders Lt. Gov Tate Reeves and House Speaker Philip Gunn both attended Bryant's private signing ceremony. "It is in states like MS where the greatest progress toward righting it is being made", she added.
Reeves did not rule from the bench but granted the temporary restraining order about an hour later, noting that clinic lawyers said a woman at least 15 weeks pregnant was scheduled to have an abortion Tuesday afternoon.
A federal judge in MS will hear arguments Tuesday over whether he should block the nation's most restrictive abortion law less than 24 hours after it took effect.
"Politicians are not above the rule of law, and we are confident this risky bill will be struck down like every similar attempt before it", Center for Reproductive Rights President and CEO Nancy Northup said in a statement obtained by the AP.
Abortion rights and anti-abortion activists square off during protests outside of Supreme Court in 2016. Anti-choice politicians have been laser-focused on enacting pre-viability abortion bans-a 20-week ban here, a six-week ban there-but all of them suffer the same problem: They're wildly unconstitutional. "The law threatens immediate, irreparable harm to Mississippians" abilities to control their "destiny and ... body, '" Reeves wrote, citing Whole Woman's Health v. Hellerstedt.
However, the law doesn't allow for exemptions in cases of rape or incest.