MOSCOW, May 24 (Reuters) - Russia outlined on Thursday a series of steps it had taken to fight kidnapping in Chechnya, a day after Amnesty International said authorities were letting murder and kidnap go unpunished in the turbulent republic.

Rights group Amnesty said in a report on Wednesday that kidnappings were still commonplace and authorities had failed to investigate and prosecute serious human rights violations.

In what appeared to be a counter to Amnesty's report, Russia's Prosecutor-General's office said kidnappings had dropped and that the fight to enforce order was showing results.

"The Chechen Republic's prosecutor has decreased the number of kidnappings in the region and improved the success rate of solving such crimes," the statement from Russia's top investigator's office said.

The office also said it had cracked down on members of the local police force who had been part of kidnap gangs.

Chechen rebels and Russia's military have fought two wars since 1994. The wars destroyed Chechnya and its capital Grozny, once the largest city in the north Caucasus, and kidnappings and murder touched almost every family in Chechnya.

Rights groups say that as many as 25,000 people died in the second war which started in 1999 and up to 5,000 people have disappeared without trace.

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