Brown and Schwarzenegger filed motions after U.S. District Judge Vaughn Walker overturned Proposition 8, California's voter-approved gay marriage ban. The court found the voter-approved ban unconstitutional.
Walker ruled the law violates federal equal protections and due process laws.
However, he agreed to block gay marriages from immediately resuming until he can consider arguments on whether to keep the ban in effect while its supporters take their appeal to the 9th U.S. Circuit Court of Appeals.
Schwarzenegger and Brown filed briefs asking Walker to immediately resume same-sex weddings in California. Earlier Friday at an event, Schwarzenegger did not indicate the filing was imminent.
"The Administration believes the public interest is best served by permitting the Court's judgment to go into effect, thereby restoring the right of same-sex couples to marry in California," wrote Kenneth C. Mennemeier, Schwarzenegger's attorney, in Friday's legal filing. "Doing so is consistent with California's long history of treating all people and their relationships with equal dignity and respect."
Brown said the overturning of Proposition 8 will likely be upheld by higher courts. He acknowledged there's a possibility they would later be invalidated, but said it's more important that the same-sex marriage ban is unconstitutional.
"Since the court has said same-sex couples have this fundamental right, then why delay for a year or two while it goes through the appellate courts?" said Brown. "As people see same-sex marriages and the families, I think there will be more acceptance."
"This is all about one more time offending the people," said Ron Prentice, chairman of Protest Marriage. "Judge Walker did it earlier this week, and now the attorney general and the governor himself are choosing to disregard the vote of the people."
Walker had given parties until Friday to file written arguments as to whether the marriages should resume. Traditional-marriage supporters want a delay during the appeals process.
It's unclear when Walker will rule on whether to let same-sex weddings to resume. Many legal experts have predicted he would not allow the weddings to resume during the appeals process, saying it would create a mess if Prop. 8 would be upheld. But no one expected Brown and Schwarzenegger to weigh in on the case.
Schwarzenegger did veto state bills given to him by the legislature to legalize same-sex weddings over the years. But he always said that courts should decide the matter.
A spokesperson for L.A. County said it will not issue same-sex marriages until the appeals process is final.
The Associated Press contributed to this report.