The uncompromising remarks in a televised New Year address were Putin's first public comments since suicide bombers killed at least 34 people in attacks less than 24 hours apart on a railway station and a trolleybus on Sunday and Monday.
But after two decades of violence in the North Caucasus, Islamist militants continue to pose a threat beyond their home region. Russia's Olympic Committee chief said no more could be done to safeguard the Games since every measure possible was already in place around Sochi, beneath the Caucasus mountains.
The bombings just ahead of Russia's biggest annual holiday followed another suicide bus blast in Volgograd in October and came little more than a month before the start of Games on whose success Putin has staked his personal reputation.
"We will confidently, fiercely and consistently continue the fight against terrorists until their complete annihilation," he said in remarks from the far eastern city of Khabarovsk, where he met victims of severe floods.
Putin travelled early on Wednesday to Volgograd, where he visited wounded victims in hospital, placed red roses at the trolleybus bombing site and held a meeting on counterterrorism efforts with senior security officials, the Kremlin said.
In the New Year address, he acknowledged "problems and serious tests" in 2013, including the Volgograd bombings, and vowed to ensure security in the year ahead.
Putin, who came to power when Boris Yeltsin announced his resignation on New Year's Eve 14 years ago, won popularity early in his presidency by crushing efforts to forge an independent state in Chechnya, but he has been unable to stop Chechen and other Islamist militants across the North Caucasus.
Police detained dozens of people in sweeps through Volgograd on Tuesday but there was no indication any were linked to the attacks, for which no one claimed responsibility.
Mourners laid flowers at the site of the bombing that tore the bus apart and left residents fearing further violence.
"I'm frightened," said Tatyana Volchanskaya, a student in Volgograd, 700 km (400 miles) northeast of Sochi. She said some friends were afraid to go to shops and other crowded places.


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