MOSCOW (Reuters) - Russia said on Wednesday it had killed the last surviving North Caucasus insurgent wanted for organizing twin bombings on the Moscow metro that killed 40 people in 2010.

Moscow is fighting an Islamist insurgency in the mountainous North Caucasus more than a decade since it re-established federal control over Chechnya after two separatist wars.

Almost daily violence is reported in the volatile region, but insurgents have also struck the Russian heartland, claiming responsibility for a suicide bombing that killed 37 at Moscow's busiest airport in 2011 and the metro bombings in 2010.

"Until today, Gusen Magomedov was the last remaining participant directly involved in the organization and carrying out of terrorist attacks on the Moscow metro in March, 2010," Russia's anti-terrorist committee said.

"Fair retribution has caught up with the last one of them," it said, adding that Russian secret service killed Magomedov overnight in the republic of Dagestan, now the center of militant violence in the North Caucasus.

Security risks in the region are in the spotlight ahead of the 2014 Winter Olympics Russia will host in the Black Sea resort of Sochi, close to the North Caucasus.

(Reporting by Gabriela Baczynska; Editing by Oliver Holmes)