State Representative Sam C. Mims, who was the chief sponsor of the law, expressed disappointment with the ruling, saying that the decision reflected a misinterpretation of its purpose.

“Abortion is still legal throughout the nation and, of course, still legal in Mississippi,” he said. “This legislation did not deal with that; it only dealt with the regulation of abortion clinics.”

Supporters of abortion rights were pleased but wary.

“The fact that the Mississippi clinic can stay open is good news, but there are a lot of other cases pending in federal courts, and it’s impossible to know if those laws will be upheld or struck down,” said Elizabeth Nash, who analyzes state laws for the Guttmacher Institute, a private research group that supports abortion rights.

Similar laws have been temporarily blocked by federal courts in Alabama, Kansas and Wisconsin while they have taken effect in Missouri, North Dakota, Tennessee, Texas and Utah.

In March, a panel from the same appeals court, composed of different judges, upheld a Texas law requiring admitting privileges, ruling that the closing of some but not all clinics within a state did not present an undue burden to women seeking abortion. About one-third of the abortion clinics in Texas have shut in the last year because of the requirement, leaving 22 open and forcing women in some parts of the state to drive more than 100 miles to obtain an abortion.

On Monday, two affected clinics in Texas are mounting a new legal challenge and clinic operators will also ask a Federal District Court to block enforcement of a more drastic requirement scheduled to take effect on Sept. 1 — that abortion clinics meet the building standards of ambulatory surgery centers. That rule could reduce the number of centers operating in the state to fewer than 10.

While the Texas and Mississippi laws were nearly identical, the judges found that the effect in Mississippi, with a single clinic, made the law there, passed by a large and bipartisan majority in 2012, constitutionally distinct from the one in Texas.