The officials filed the motions after U.S. District Judge Vaughn Walker previously overturned California's voter-approved gay marriage ban, known as Proposition 8.
Resuming gay marriage "is consistent with California's long history of treating all people and their relationships with equal dignity and respect," Schwarzenegger said in his legal filing.
Walker ruled Wednesday the ban 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.
Brown, a candidate for governor, said that ruling means it's time for gays to begin marrying again.
"While there is still the potential for limited administrative burdens should future marriages of same-sex couples be later declared invalid, these potential burdens are outweighed by this court's conclusion, based on the overwhelming evidence, that Proposition 8 is unconstitutional," Brown said in his legal filing.
It was unclear when Walker would issue a ruling on the possible resumption of same-sex marriages.
The outcome in the appeals court could force the U.S. Supreme Court to confront the question of whether gays have a constitutional right to wed.
Currently, same-sex couples can legally wed only in Massachusetts, Iowa, Connecticut, Vermont, New Hampshire and Washington, D.C.
California voters passed Proposition 8 five months after the state Supreme Court legalized same-sex unions and an estimated 18,000 same-sex couples already had tied the knot.
Walker presided over a 13-day trial earlier this year that was the first in federal court to examine if states can prohibit gays from getting married without violating the constitutional guarantee of equality.
Supporters argued the ban was necessary to safeguard the traditional understanding of marriage and to encourage responsible childbearing.
Opponents said that tradition or fears of harm to heterosexual unions were legally insufficient grounds to discriminate against gay couples.