Kennedy turned away the request on Sunday with no additional comment.
Same-sex marriage opponents asked him to step in on Saturday, a day after the federal appeals court in San Francisco allowed same-sex marriages to go forward. Numerous weddings were performed at San Francisco City Hall following the court decisions.
The opponents said the appeals court had acted about three weeks too soon. Proposition 8 supporters could continue their efforts to halt gay marriage by filing their request with another Supreme Court justice.