MOSCOW (Reuters) - Russian President Vladimir Putin has signed off on tougher anti-terrorism laws ahead of the 2014 Winter Olympics that could oblige relatives to pay for any damage caused by militants fighting a separatist campaign in southern Russia.

The February games will take place around the Black Sea resort of Sochi, a few hundread kilometres from the mountainous North Caucasus region where rebels are fighting to carve out an Islamic state.

Moscow has cracked down on the Islamist insurgency in Dagestan, the epicentre of North Caucasus violence. But an Oct 21 suicide attack - staged outside the region but blamed on a woman from Dagestan - highlighted the threat to security.

The new law, which Mr Putin signed on Nov 2, according to documents published on Sunday on the Russian authorities' legal website, introduces prison terms of up to 10 years for undergoing training "aimed at carrying out terrorist activity".

"Compensation for damage... caused as a result of a terrorist act is covered... with the means of the person that committed a terrorist act, and also the means of close relatives, relatives and close acquaintances if... they obtained money, valuables and other property as a result of terrorist activity," the law also says.

The law, originally proposed to Parliament by the Kremlin, also allows for the seizure of property of relatives and close acquaintances of suspected militants if they fail to provide documents proving their rightful acquisition.

Rights activists accuse authorities of grave human-rights violations in the North Caucasus and say such heavy handed tactics only fuel anger and resentment among local inhabitants.