Editor's note: This story has been updated throughout.

Texas Attorney General Ken Paxton, who was facing possible contempt of court charges, vowed on Monday that the state would revise its policies in the next week to allow same-sex couples to obtain amended death certificates.

The move came hours after Paxton asked U.S. District Judge Orlando Garcia to quash an order requiring him and a top state health official to attend a contempt of court hearing on Wednesday. That hearing stemmed from a ruling last week by U.S. District Judge Orlando Garcia ordering state officials to recognize the same-sex marriage of a Conroe resident by naming him as the surviving spouse on his late husband's death certificate.

Garcia also ruled that Paxton and Kirk Cole, interim commissioner of the Texas Department of State Health Services, should appear in court in San Antonio to determine whether they should be held in contempt for refusing to amend the death certificate.

In his ruling, Garcia said the state had violated a July decision that prohibited state officials from enforcing Texas' now-defunct ban on same-sex marriages. That order was issued shortly after the U.S. Supreme Court ruled that states must recognize same-sex marriages.

A spokeswoman for the AG’s office confirmed the hearing had been canceled “while DSHS finalizes guidelines for the issuance of death certificates.”

A hearing is now scheduled for Sept. 10 to allow the state to finalize its revised policies.

Following Garcia's order last week, the state reissued the death certificate naming Stone-Hoskins as a surviving spouse of his husband, who died in January. The couple had wed in New Mexico last year, but Stone-Hoskins was not initially named on the death certificate because the state did not recognize same-sex marriages at the time.

Attorney Neel Lane, who has represented the same-sex couples in the lawsuit, said the AG “advised the judge” during a telephone hearing on Monday that the state health department, which oversees vital records, would issue new policy guidelines this week “making clear that same-sex couples are entitled to amended death certificates and amended birth certificates to the same extent as opposite-sex couples.”

In light of the Supreme Court’s ruling, gay rights activists had said they would pursue consistent parental rights on Texas birth certificates, which only allow for a mother and a father to be listed.

That means, for instance, when a woman has a child, her same-sex spouse is not automatically listed on the birth certificate — and considered the child's parent — as a male spouse would be. The non-biological parent has to adopt the child later to gain parental rights.

Same-sex couples adopting a child run into the state's requirements for supplemental birth certificates, which are issued to establish parental rights for adopters. Texas supplemental certificates allow for two parents to be listed, "one of whom must be a female, named as the mother, and the other of whom must be a male, named as the father." As a result, only one parent is listed for same-sex couples.

In the brief filed Monday morning, state attorneys had argued that Paxton and Cole should not be required to appear in court because other officials "have been intimately involved in the details" of naming John Stone-Hoskins as the surviving spouse on the death certificate for his late husband, James.

"Under well-established precedent, a high-ranking government official should not be compelled to personally appear and testify absent extraordinary circumstances, which are present only when a high-ranking official has personal knowledge of information that is essential to a case and that evidence cannot be obtained from another source," state attorneys wrote.

They offered to instead send a deputy attorney general and deputy general counsel for the state health department, who have also been involved in "developing a policy" regarding the issuance of death certificates in light of the Supreme Court's ruling on same-sex marriages.

In a brief filed Wednesday afternoon, Stone-Hoskins' attorneys had asked the court to dismiss Paxton's request and pursue contempt of court charges, alleging Paxton has "virtually incited" state employees to "ignore and resist" the same-sex marriage rulings.

Stone-Hoskins' attorneys added that Paxton, who they describe as the "lead cheerleader," and Cole are behind "contemptuous acts," including denying same-sex couples to both be listed on their children's birth certificates.

"Paxton and Cole’s contemptuous attitude and acts have consequences far beyond the single case of John Stone-Hoskins, whose situation is hardly unique," the attorneys wrote, adding that Garcia should exercise "his inherent power of contempt" to ensure state officials abide by same-sex marriage rulings.