Mississippi's governor has signed a law banning most abortions after 15 weeks' gestation, the tightest restrictions in the US.
Phil Bryant has frequently said he wants Mississippi to be the "safest place in America for an unborn child".
House Bill 1510's only exceptions are if a foetus has health problems making it "incompatible with life" outside the womb at full term, or if a pregnant woman's life or a "major bodily function" is threatened by pregnancy.
Pregnancies resulting from rape and incest are not exempted.
The state's only abortion clinic and one of the physicians who practises there filed a federal lawsuit in Jackson, an hour after it was signed into law.
In a suit handled by the Centre of Reproductive Rights, the Jackson Women's Health Organisation said the measure is unconstitutional and should immediately be struck down.
The suit says the clinic performed 78 abortions in 2017 when the foetus was identified as being 15 weeks or older. That is out of about 2,500 performed statewide, mostly at the clinic.
The lawsuit says federal courts have ruled women have the right to an abortion before a foetus can live on its own outside the womb.
The Mississippi measure is specifically designed to challenge those rulings, trying to get courts to rule states can restrict abortion before viability.
Mississippi previously tied with North Carolina for the nation's strictest abortion limits at 20 weeks.
Both states count pregnancy as beginning on the first day of a woman's previous menstrual period. That means the restrictions kick in about two weeks before those of states whose 20-week bans begin at conception.
"We certainly think this bill is unconstitutional," said Katherine Klein, equality advocacy co-ordinator for the American Civil Liberties Union of Mississippi.
"The 15-week marker has no bearing in science. It's just completely unfounded and a court has never upheld anything under the 20-week viability marker."
The bill was drafted with the assistance of conservative groups including the Mississippi Centre for Public Policy and the Alliance Defending Freedom.
"We're thrilled that Mississippi lawmakers are taking a step to protect the basic right to life, as well as protecting maternal health," said Jameson Taylor, acting president of the Mississippi Centre for Public Policy.
Both Republican-controlled chambers passed the bill overwhelmingly in early March, by a vote of 35-14 in the Senate and 76-34 in the House.
The US Senate failed to pass a 20-week abortion ban bill in January. With 60 Yes votes required to advance, the bill failed on a 51-46 vote.