The tough talk came a day after the deadliest attack on the Russian capital in six years fueled fears of a broader offensive by rebels based in the North Caucasus and underscored the Kremlin's failure to keep militants in check.
Putin told a meeting on transport security that surveillance cameras could not prevent terrorist attacks but might help police identify their organizers.
"In this case, we know they're lying low, but it's a matter of honor for law enforcement bodies to scrape them from the bottom of the sewers and into the daylight," he said.
The colourful language fit Putin's tough image.
In 1999, as he led Moscow into a war against Chechen separatists that sealed his rise to power, he vowed to pursue terrorists everywhere and "rub them out in the outhouse." Moscow observed a day of mourning on Tuesday for the victims of the blasts, which authorities said were set off by female suicide bombers linked to the North Caucasus - a string of heavily Muslim provinces that includes Chechnya.
Flags flew at half-mast and sombre Muscovites - some sobbing, some crossing themselves - laid flowers and lit candles at the stations hit by Monday's rush-hour blasts.
Grieving relatives identified victims at central Moscow's Morgue Number Two.
Eyes brimming with tears, an elderly man said his son usually drove to work but had his license confiscated recently.
"So he went by metro and he died," said the man, who identified himself as Vladimir Petrovich, giving his patronymic but not his last name.
In less earthy terms than Putin, who steered him into the presidency in 2008 and is seen as the dominant partner in Russia's ruling tandem, Medvedev also vowed justice.
"We have destroyed terrorists and will destroy them," he said in televised remarks at a meeting on civil rights.
But he accentuated the hurdles the Kremlin faces in uprooting an Islamic insurgency in the North Caucasus, saying the government must tread carefully in the turbulent region and tackle the root causes.
"People want a normal human life no matter where they live - in central Russia, the Caucasus or somewhere else," he said.
"It's up to federal authorities and the authorities in the Caucasus region to create these conditions." The war Putin launched in 1999 drove separatists from power in Chechnya, but simmering violence has escalated in the past two years in Chechnya and neighboring Dagestan and Ingushetia.
Rights groups contend that poverty, corruption and abuse of power is fueling the insurgency.
In recent years, attacks had been largely limited to the North Caucasus.
With police patrols increased on Tuesday, commuters warily entered Moscow's metro system the morning after the blasts on packed trains at the central Lubyanka and Park Kultury stations.
"When I was riding the metro in today, somebody's electronic watch started beeping and I thought, "That's it," said Katya Vankova, a business student.
Memorials were set up at both stations. At Park Kultury, people left red carnations and tied white ribbons to a stand on the platform close to where the bomb went off.
A young woman died of her injuries on Tuesday, bringing the death toll to 39, Andrei Seltsovsky, the chief of Moscow's health department, said on state-run Rossiya 24 television.
He said 71 other people were still in hospital, five of them in critical condition. Officials said the bombs that caused the carnage were packed with bolts and iron rods.
