The Fifth U.S. Circuit Court of Appeals on Tuesday upheld a Texas law that requires women seeking an abortion to have a sonogram exam and to listen to a physician's detailed description of the fetus, including whether it has developed limbs or internal organs.

Supporters of the law, enacted last year, say it is designed to ensure that women are fully informed about abortions and, ultimately, to discourage them from undergoing the procedure. It requires all women seeking abortions to have a sonogram, also known as an ultrasound...