Plaintiffs in a case challenging Utah's gay marriage ban have asked the U.S. Supreme Court to reject a request for an emergency stay in a lower court's ruling declaring the state's ban invalid.

On Tuesday, the Utah Attorney General's Office filed its fifth request for a stay in the ruling as an appeal moves forward. U.S. District Judge Robert Shelby, who issued the ruling on December 20, and the 10th Circuit Court of Appeals denied the state's previous request.

In their filing, plaintiffs, three gay couples, argued that Utah's Amendment 3 “cannot withstand a heightened level of constitutional scrutiny.”

“The District Court also found that the challenged laws warrant heightened equal protection scrutiny because they discriminate against Respondents on the basis of sex,” the 61-page document states. “However, the District Court concluded that it need not analyze why Applicants were unable to meet that heightened burden because the laws failed even under rational basis review.”

“In addition, the District Court found that the laws harmed the children of same-sex parents in Utah 'for the same reasons that the Supreme Court found that DOMA harmed the children of same-sex couples,'” plaintiffs argued.

In filing its 25-page application for a stay, Utah officials argued that they were attempting to avert “irreparable harm” to gay couples and their families.

“The State's responsibility for the welfare of all its citizens makes it relevant, as well, that Respondents and any other same-sex couples who choose to marry during the period before the Tenth Circuit and this Court resolve this dispute on the merits will likely be irreparably harmed without a stay. They and their children will likely suffer dignitary and financial losses from the invalidation of their marriages if appellate review affirms the validity of Utah's marriage laws,” the state wrote.

More than 1,000 gay couples have married in the state in the wake of the ruling.