Texas Governor Greg Abbott, a Republican, on Thursday reiterated his support for the state's ban on gay marriage.

In a statement, Abbott said that he was responding to “the ruling by a Travis County district judge” but didn't discuss specifics in the case.

“Article 1, Section 32 of the Texas Constitution defines marriage as consisting ‘only of the union of one man and one woman’ and was approved by more than three-quarters of Texas voters,” he said. “I am committed to ensuring that the Texas Constitution is upheld and that the rule of law is maintained in the State of Texas.”

Abbott, who was sworn in as the 48th governor of Texas on January 20, defended the ban in court in his former role as state attorney general

(Related: TX AG Greg Abbott: Gay marriage ban promotes “responsible procreation.”)

On Thursday, two Austin women became the first gay couple to marry in the state after they received a marriage license in Travis County.

Attorney General Ken Paxton has asked the Texas Supreme Court to void the couple's marriage license.

(Related: Ken Paxton asks Texas Supreme court to void lesbian couple's marriage license.)