Kennedy made the decision on Sunday. He did not release any additional comment.
Same-sex marriage opponents filed an emergency motion on Saturday asking Kennedy to step in and intervene. One day earlier, the 9th Circuit Court of Appeals lifted a stay on same-sex marriages in California, allowing gay marriages to resume immediately. Numerous weddings were performed at San Francisco City Hall following the court decision.
The opponents said the appeals court acted prematurely and unfairly when it allowed gay marriage to resume. Proposition 8 supporters could continue their efforts to stop gay marriage by filing their request with another Supreme Court justice.
The U.S. Supreme Court cleared the way for same-sex marriages in California on Wednesday after ruling that Proposition 8 defenders did not have the right to appeal lower court rulings.
The Supreme Court also struck down a key provision of the Defense of Marriage Act that denied benefits to legally married gay couples. The ruling means that legally married same-sex couples should get the same federal benefits as heterosexual couples.
Los Angeles County plans to start issuing marriage licenses to same-sex couples on Monday.
Meanwhile, thousands of people turned out for the 43rd annual pride parade in San Francisco on Sunday. Large crowds also attended parades in New York, Chicago, Minneapolis-St. Paul, Seattle and St. Louis.
Many local registrar offices will open for the first time Monday since the ban on gay marriages in California was lifted.
West Hollywood City Council members and other city officials will be temporarily deputized to help with the expected rush of same-sex couples flocking to City Hall to get married."If one couple shows up or 100 couples show up, it'll be great," said West Hollywood Councilmember John D'Amico. "Just stepping on the right foot showing L.A. County and the state of California, the whole country, that West Hollywood is a place that's safe for gay and lesbian couples to come and get married. Anyone is welcome here and everyone should get married and live their happy lives."
Ceremonies will be performed free of charge on a first-come, first-serve basis from 1 p.m. until 7 p.m. on Monday. Couples must have a license issued by the Los Angeles County Registrar-Recorder before being married.
The Associated Press contributed to this report.