The high court's written ruling on whether the voter initiative should be struck down will be due 90 days later.
The measure, enacted by voters on Nov. 4, amended the state Constitution to provide that "only marriage between a man and a woman is valid or recognized in California."
It overturned a decision in which the court said by a 4-3 vote in May that gay and lesbian couples have a constitutional right to marry.
The panel is now considering three lawsuits filed by same-sex couples and a coalition of cities and counties to challenge the ban.
The lawsuits claim the measure is so sweeping it is a constitutional revision, which would require approval of two-thirds of the Legislature as well as a majority of voters.
The court has said it will rule on both whether Proposition 8 is constitutional and, if so, whether it retroactively invalidates the estimated 18,000 same-sex marriages performed in California before Nov. 4.
The justices in today's order allocated an unusual three hours for the arguments in their State Building courtroom beginning at 9 a.m. on March 5. Cases are normally allotted only half an hour per side.
Lawyers for each set of plaintiffs will each get 30 minutes. The plaintiff groups are six same-sex couples and a civil rights organization, Equality California; a seventh couple that filed a separate lawsuit; and 15 cities and counties led by the cities of San Francisco and Los Angeles and Santa Clara County.
Starr and Pugno had asked for extra time because their clients are the only party in the case fully defending Proposition 8.
In a surprise move, California Attorney General Jerry Brown, whose job is to defend the state's constitution and laws, in December submitted arguments both for and against the measure and concluded that the court should strike it down.
Brown told the court in a filing that he doesn't think that Proposition 8 is a constitutional revision or that it violates the constitutional separate of powers. But he said he believes it is unconstitutional because it violates the inalienable right to liberty.
The court gave Brown 30 minutes, but instructed him to "divide his time between his arguments in support of, and his argument in opposition to, the validity of Proposition 8."
Groups that filed friend-of-the-court briefs will not be given time to argue unless one of the official parties in the case agrees to give up part of its time.
At least 63 friend-of-the-court briefs were filed by individuals and coalitions of groups, some representing dozens of other organizations, including religious groups, law professors, business groups, labor organizations and civil rights groups.
Twenty of the friend-of-the-court briefs supported Proposition 8, while 43 favored striking it down.
Kate Kendell, legal director of the San Francisco-based National Center for Lesbian Rights, which filed the first lawsuit on behalf of same-sex couples, said, "Proposition 8 represents a tremendous threat to the rights of every minority group in California."
Kendell said, "As our legal team prepares for oral argument before the California Supreme Court, we are hopeful that the court will end the short life of this draconian measure."
Pugno and Starr have argued in court filings that Proposition 8 represents the will of the people and is well within the initiative power.
They wrote in their final brief last month, "Proposition 8 is a moderate measure that represents a deeply rooted, multigenerational judgment of the people of California about the definition of marriage."