The petition to the high court states that whether marriage should be redefined to include same-sex couples is "a profoundly important question" and "a matter of great debate in our nation."
The appeal argues that individual states should be allowed to define marriage because the U.S. Constitution neither requires nor condemns gay marriage.
"Rather, it leaves the definition of marriage in the hands of the people, to be resolved through the democratic process in each state," the petition asserts.
Proposition 8, enacted by state voters in 2008, provides that "only marriage between a man and woman is valid or recognized in California."
It has been declared unconstitutional by a federal trial judge and a federal appeals court in San Francisco, but the measure has been left in place and same-sex marriages have been blocked during the appeals process.
The petition for a hearing before the high court was filed by the initiative's sponsors and their committee, Protect Marriage.
The Supreme Court is expected to decide this fall whether to take up the case. If it decides to hear the appeal, its decision would be expected by the end of June 2013.
If the panel does not take up the appeal, then a ruling by the 9th U.S. Circuit Court of Appeals earlier this year striking down Proposition 8 would become the final decision in the case, and same-sex weddings could resume.
Gay and lesbian marriages were briefly legal in California for several months in 2008 until voters approved Proposition 8 in November of that year. During that time, 18,000 same-sex couples married, and the California Supreme Court has ruled that those marriages remain valid.
The federal court rulings have been made in a federal civil rights lawsuit filed in 2009 by two same-sex couples.