The parade is scheduled to take place in the city center on May 27, the 13th anniversary of the decriminalization of homosexuality in Russia.
Earlier this year,Mayor Yuri Luzhkov's office said the gay parade could not take place because the proposed May 27 event had "evoked outrage in society, in particular, among religious leaders."
Under Russian law, permission for public rallies must be applied for no earlier than two weeks ahead. A decision is usually issued within 72 hours, the AP reports.
Rights groups have condemned the city hall's stance as a violation of civil rights and expressed concern about recent actions targeting gay-friendly bars by skinheads and religious protesters as evidence of rising homophobia.
On the night of April 30, several hundred protesters, including skinheads, elderly Russian women holding religious icons and nationalists, disrupted a gay night at a Moscow nightclub, throwing eggs, tomatoes and plastic bottles at clubbers and forcing them to be evacuated by bus.
Approximately 5-8 percent of Russia's 143-million-strong population is gay and lesbian, according to gay rights activists.
Alexeyev said that if the mayor's office denied permission, the rally would take place anyway.
The troops of the Southern and Western military districts will begin to return from Russia's southern borders to the points of their permanent deployment starting April 23