* Former parliamentarian detained twice in 24 hours
* Putin under fire abroad over "gay propaganda" law (Adds second detention)
By Catherine Koppel
SOCHI, Russia, Feb 17 (Reuters) - A transgender former member of Italy's parliament was detained by Russian police for the second time in 24 hours on Monday for trying to stage a gay rights protest at the Winter Olympics.
Vladimir Luxuria said she was led away by two men in plain clothes on Sunday when she held up a sign saying "Gay is OK" in Russian in the Sochi Olympic Park and was held for about three hours.
She was allowed into the Olympic Park again later on Monday but barred from watching an ice hockey match because she was wearing a rainbow headdress - the colours of the lesbian, gay, bisexual and transgender movement - and had a gay pride flag.
Luxuria said she was protesting against a law signed by President Vladimir Putin last year banning the spread of "gay propaganda" among minors. Critics say it discriminates against gays and that it has fuelled violence against homosexuals.
"I think it is important ...(to have) the opportunity to talk internationally about these things because otherwise these things happen in Russia and nobody knows, nobody cares," Luxuria said after stepping off the stage at a gay cabaret bar in Sochi.
"They think: 'Well, it's not in our country, it's far away, it's in Russia, who cares?'"
She said she had been treated with respect while in detention on Sunday but was told by the police that she could not promote pro-gay slogans in public.
The police and the Russian organisers of the Games said the police had no formal record of her detention. International Olympic Committee spokesman Mark Adams said: "We hope that the Games will not be used as a platform for demonstrations."
TWO YEARS IN PARLIAMENT
A man was detained separately in Sochi on Monday for staging a solo protest against the jailing of an environmentalist who campaigned against Olympic construction work. A lawyer said the man, David Khakim, had been sentenced by a local court to 30 hours community service.
While the Games are under way, protests in Sochi are allowed only in a specially designated area in a park about 20 minutes by train from the nearest sports venues.
Putin, who says the "gay propaganda" law is needed to protect children, wants to ensure protests do not overshadow the Games after months of international criticism of the "gay propaganda" law in the run-up to the Olympics.
Luxuria, 48, was born a male but wears women's clothes although she has not had sex-change surgery. She represented the Communist Refoundation Party in parliament for two years until April 2008, and is a prominent defender of gay rights.
"I think this is so important. For me, I've experienced in my childhood what it means to be beaten up or abused for the fact that I'm transgender," Luxuria said. "If I stop wearing the colours of the rainbow, just because somebody took away a flag from me, that means that these people win."
Putin has said gay athletes, officials and spectators are welcome at the Games and will not be discriminated against.
Gay rights groups called for a boycott of the Games over the law, and U.S. President Barack Obama sent a delegation to Sochi that included gay officials. Obama did not attend himself. (Additional reporting by Anna McIntosh and Karolos Grohmann, Writing by Timothy Heritage)