Attorney Theodore Olson made the argument in a letter to U.S. District Judge Vaughn Walker.
Walker is presiding over a nonjury trial in which two gay and lesbian couples claim Proposition 8, California's voter-approved ban on same-sex marriage, violates their federal constitutional rights.
Walker conducted the trial in January, heard closing arguments last month, and is currently considering a decision. He has not indicated when he will rule.
Olson wrote in the letter that U.S. District Judge Joseph Tauro of Boston "considered and rejected many of the same irrational justifications asserted by proponents in defense of Proposition 8."
The rulings show that "none of the unfounded rationales asserted by proponents in justification of Proposition 8 can sustain this discriminatory law," Olson argued.
Tauro's decisions struck down a provision of the 1996 federal Defense of Marriage Act that denied federal benefits to same-sex married couples.
He ruled that the law violated legally married gay and lesbian couples' constitutional right to equal treatment. Massachusetts is one of five states that allow same-sex marriage.
Among other conclusions, Tauro said arguments that heterosexual marriage is better for children and is strengthened by banning same-sex marriage are unfounded and are not a rational basis for denying benefits to same-sex couples.
Olson quoted those conclusions in the letter to Walker along with a third conclusion in which Tauro said moral disapproval of homosexuality is not a legitimate justification for a law.
Olson and other lawyers for the same-sex couples had argued those same points in the Proposition 8 trial before Walker.
A decision by a federal judge in one state is not binding on U.S. judges in other states, but it can be cited as support by other judges.
If Tauro's decision is appealed to the U.S. Supreme Court, however, the high court's conclusions will be binding nationwide. The Obama Administration has not yet said whether it will appeal.
A spokeswoman for the proponents of Proposition 8 and their campaign committee, ProtectMarriage.com, was not immediately available for comment on Olson's letter.
Their lawyers have argued that state voters had a rational basis for believing that heterosexual marriage promotes "naturally procreative relationships between men and women to provide for the nurture and upbringing of the next generation."
Proposition 8 attorney Charles Cooper argued at the close of the trial that the purpose of marriage is procreation and said that definition is "fundamental to the very existence and survival of the human race."
Proposition 8, approved by a 52 percent majority of state voters in November 2008, provides that "only marriage between a man and a woman is valid or recognized in California."
It was enacted as an amendment to the state Constitution and thus overturned a May 2008 decision in which the California Supreme Court said the state document provided a right to same-sex marriage.
The lawsuit before Walker, filed by Kristin Perry and Sandra Stier of Berkeley and Paul Katami and Jeffrey Zarrillo of Burbank, focuses on federal rather than state constitutional rights.
The trial has been the nation's first federal trial on a challenge under the U.S. Constitution to a state law banning gay and lesbian marriage.