The uncompromising remarks in a New Year's Eve address were Mr Putin's first public comments since suicide bombers killed at least 34 people in attacks on a railway station and a trolleybus on Sunday and Monday.
The bombings raised fears of further attacks before and during the Winter Olympics, which take place in in less than six weeks' time in the Black Sea resort of Sochi.
"I am certain we will fiercely and consistently continue the fight against terrorists until their complete annihilation," the Russian president said, adding: "Dear friends, we bow our heads before the victims of cruel terrorist acts."
Mr Putin - who first became president when Boris Yeltsin stepped down and named him to the post exactly 14 years ago yesterday - has been unable to crush Islamist militants in the Muslim provinces of the North Caucasus.
Police yesterday detained dozens of people in sweeps through Volgograd, although there was no indication any were connected to the attacks, for which nobody has claimed responsibility.
Volgograd - formerly Stalingrad - is a city of about one million and a transport hub for an area of southern Russia that includes Chechnya and the other mostly Muslim provinces of the North Caucasus, where the insurgency generates deadly violence almost every day.
Mr Putin has staked his prestige on the Olympic Games in Sochi, which lies at the western edge of the Caucasus Mountains and within the strip of land the insurgents want to carve out of Russia and turn into an Islamic State.
Mr Putin ordered increased security nationwide after the attacks, the deadliest outside the North Caucasus since January 2011, when a suicide bomber from a province neighnouring Chechnya killed 37 people at a Moscow airport.
Investigators said they believed a male suicide bomber was responsible for Monday's morning rush-hour blast, which turned a trolleybus into a twisted wreck and left bodies lying in the street.
In Sunday's attack on the station, authorities initially described the bomber as a woman from Dagestan, but later said the perpetrator may have been a man.
Citing unnamed sources, the Interfax news agency said the suspected attacker in Sunday's blast was an ethnic Russian convert to Islam who had moved to Dagestan and joined militants there early in 2012.
The violence has raised fears of a concerted campaign before the Olympics.
Intended to showcase how Russia has changed since the collapse of Soviet communism in 1991, the Games have also been a focus for complaints in the West, and among Russian liberals, that Mr Putin has stifled dissent and encouraged intolerance.
Last month, Mr Putin freed jailed opponents - including oil tycoon Mikhail Khodorkovsky and members of the Pussy Riot punk band - in what critics said was an effort to disarm Western criticism and improve his image.
In an online video posted in July, the Chechen leader of insurgents who want to carve an Islamic state out of mainly Muslim provinces south of Volgograd, urged militants to use "maximum force" to prevent the Games going ahead.
International Olympic Committee President Thomas Bach condemned the "despicable attack on innocent people" and said he had written to Mr Putin to express condolences and confidence that Russia would deliver "safe and secure games in Sochi".