* Georgian legislation to irk Russia
* Circassians say 19th c. killings were genocide
* Strikes at heart of growing row over 2014 Winter Olympics
By Margarita Antidze
TBILISI, May 20 (Reuters) - Georgia's parliament branded the 19th century killings of a Muslim minority by Russia's tsarist forces genocide in a resolution on Friday likely to strain Tbilisi's already troubled ties with Moscow.
Originally from the northwest Caucasus, Circassians say 1.5 million of their ancestors were systematically killed in a Russian military campaign in 1860-64 to conquer the Caucasus mountain area on the southern border of today's Russia.
The deaths were recorded by Russian imperial historians in 1864. No nation has recognised them genocide.
"We as a representatives of Georgian people should end the 150-year long sufferings of Circassians and restore their rights," said Nugzar Tsiklauri, the head of a parliamentary committee for relations with diasporas and Caucasus nations.
The move is likely to strain relations between Russia and Georgia, which have yet to recover from a five-day war in 2008 over the Moscow-backed separatist province of South Ossetia.
The resolution could increase tension over the 2014 Winter Olympics, which Russia is hosting in Sochi, a resort city in what the Circassians consider their historic homeland.
Members of the Circassian diaspora are demanding the Sochi Games be cancelled or moved unless Russia apologises for what they say was genocide against their ancestors. Some Circassian leaders are demanding autonomous territory within Russia.
Earlier this year Russian President Dmitry Medvedev pointed to Georgia as a potential security threat to the games.
Tsiklauri presented a draft of the resolution, which said: "Killings and deportations of Circassians during the Russian-Caucasian War should be recognised as genocide and ethnic cleansing."
Deportations and turmoil led many Circassians south to Turkey and elsewhere, and their seven million or so descendants are spread across the world from the United States to Jordan to Israel. About 700,000 remain in the northwest Caucasus.
The closest the Russian government has come to apologising for the bloodshed was in 1994, when President Boris Yeltsin acknowledged that resistance to tsarist violence was legitimate.
(Editing by Thomas Grove and Paul Taylor)
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