Irina Fedotova and Irina Chapitko tried to marry at a register office in central Moscow but were told that Russian law only permitted heterosexual marriage.
"We cannot accept your request," Svetlana Potamyshneva, head of the register office, told the couple in the presence of journalists and television crews who had been invited by gay activists to cover the event.
"Point 3 of Article 1 of the Family Code of Russia stipulates that the regulation of family relations must adhere to the principle of a voluntary union between a man and a woman," she added.
Fedotova, dressed in a white suit with a black bow tie, told reporters afterward: "We are like everyone else and we have the same rights as heterosexuals."
Homophobia is widespread in Russia, which considered homosexuality a crime until 1993 and ceased to classify it as mental illness only in 1999.
But gay activists have been seeking to publicise the issue in the run-up to this week's Eurovision Song Contest, the campy annual musical extravaganza with a strong gay following that is being held in Moscow this year.
Activists plan to hold a gay pride parade on Saturday, the day of the Eurovision final, despite a ban by the Moscow city government and the fact that earlier gay rallies were violently attacked by religious nationalists.
Gay activists have been particularly critical of Moscow Mayor Yury Luzhkov, who has denounced the gay pride parades as "Satan's work" and called homosexuality immoral.
"When the Moscow mayor is banning the event and saying that it is Satan's gathering... after that obviously the level of homophobia grows enormously," gay activist Nikolai Alexeyev said at Tuesday's unsuccessful wedding.
Alexeyev, the creator of the GayRussia.ru website and an organiser of previous gay pride parades, also said that activists would help pay for Fedotova and Chapitko to fly to Canada to register their marriage.