The session highlighted a deep divide among the nine justices. Chief Justice John Roberts led the Republican- appointed wing in suggesting states shouldn't be required to recognize gay marriages.
"I'm not sure that it's right to view this as excluding a particular group," Roberts said. "When the institution of marriage developed historically, people didn't get around and say let's have this institution, but let's keep out homosexuals. The institution developed to serve purposes that, by their nature, didn't include homosexual couples."
The four Democratic-appointed justices voiced support for gay marriage. Justice Elena Kagan questioned the contention by proponents of Proposition 8 that marriage was designed to foster and regulate procreation. She asked whether the state could bar any marriages when both people are over 55.
"I can just assure you, if both the woman and the man are over the age of 55, there are not a lot of children coming out of that marriage," Kagan said.
Kennedy aimed questions at both sides. He suggested that children of same-sex couples suffer "immediate legal injury" from California's ban.
"They want their parents to have full recognition and full status," Kennedy said. "The voice of those children is important in this case, don't you think?"
At the same time, Kennedy said the reasoning of the federal appeals court that struck down California's ban was "very odd."
Kennedy has been a champion of gay rights in past cases, writing the 2003 decision that said states can't criminalize gay sex acts. Even so, he made clear in that case that he wasn't passing judgment on same-sex marriage.
The case is the first of two gay-marriage arguments this week for the court, which Wednesday will take up the 1996 U.S. Defense of Marriage Act, known as DOMA. That law defines marriage as a heterosexual institution, barring legally married gay couples from claiming the federal benefits available to opposite-sex married couples.