The law, passed in October, would specifically look at the possibility that real estate or other family assets were acquired illegally by a family member involved in terrorist activities.
The law is the latest effort by Moscow to root out the long-running insurgency in the North Caucuses, Russia's RIA Novosti news agency said.
The legislation signed Sunday boosts the penalty for taking part in so-called terrorist training at insurgent camps to 10 years in prison. Anyone convicted of organizing a terrorist network can now get 20 years in prison.
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