* Russia working hard on security at Games
* Sochi borders volatile North Caucasus region
* Medvedev says more measures needed to make Games memorable
By Stephen Adler and Timothy Heritage
MOSCOW, Nov 1 (Reuters) - The Russian government and security services will overcome security threats and can guarantee safety at the 2014 Winter Olympics in the Black Sea resort of Sochi, Prime Minister Dmitry Medvedev said.
In an interview with Reuters, Medvedev said Russia had taken a number of safety measures around the city, which borders the volatile North Caucasus region where Islamist insurgents wage nearly daily violence.
"A number of threats exist in our country, so everyone is working as hard as possible - the special forces are working, and the government as a whole is trying to guarantee the absolute safety of the Olympic Games," he said on Thursday.
"And I believe that's what will happen. But it's clear that we should take a number of other decisions to make sure that these Games are held without a hitch, so that they will be remembered as a spectacular sporting event."
He did not specify what those measures were.
Spending on the February Games is expected to pass $50 billion, and they are a priority for President Vladimir Putin who wants to use it to showcase the country's modern face to the world two decades after the fall of the Soviet Union.
Thomas Bach, the head of the International Olympic Committee (IOC), visited Sochi to inspect preparations this week and praised the work and said he was sure the Games would be "magnificent".
Security services have installed video cameras around the city and plan to use drones at the Games to keep watch over the sprawling venues that reach from the Black Sea coast, where skating events will be held, to the Caucasus Mountains.
Russian police are also planned to be stationed along the perimeter between Sochi and the mountainous North Caucasus, where insurgents are fighting to establish an Islamic state.
The insurgency, rooted in two separatist wars in Russia's province of Chechnya, has spread through the North Caucasus, and Dagestan, some 600 kilometers away from Sochi, has become the focal point of violence.
A deadly suicide bombing in southern Russia on Oct.21, blamed on a Muslim woman from the North Caucasus, highlighted increased the security risks Sochi faces.
Medvedev said that the initial idea of holding the Olympics in the sub-tropical city of Sochi, had struck him as "extravagant", but that he was convinced the Games would be a success.
"The city of Sochi is located in the subtropics, and it's hosting the Winter Olympics. That in and of itself is quite interesting. I won't hide the fact that when the idea was conceived, even to me it seemed rather extravagant," he said.
"But it happened that they chose Sochi, and I am sure that they will be a very interesting Games."