Nemtsov had been one of Putin's harshest critics and had been arrested several times for speaking against the President's government.
The 55-year-old opposition leader was gunned down Friday night in Moscow as he walked across a bridge about 100 meters (330 feet) from the Kremlin with his girlfriend, Ukrainian model Anna Duritskaya
Nemtsov isn't the first of Putin's critics to turn up dead
, with others including Anna Politkovskaya (who was fatally shot) and Alexander Litvinenko (who was poisoned). The Kremlin has staunchly denied accusations that it's targeting political opponents or had anything to do with the deaths.
The Russian leader has condemned Nemtsov's killing and ordered three law enforcement agencies to investigate, the Kremlin has said. He also wrote to Nemtsov's mother, saying he shared her grief, and promised to bring those behind the killing to justice.
Yet those expressions came in Kremlin statements. Wednesday was the first day Putin spoke at length on the subject, remarks that were reported by state media outlets.
Referring to "the daring killing of Boris Nemtsov in the very heart of our capital city," he said, "Russia should be made secure, at last, from the disgrace and tragedies of (this) kind."
The President added, according to the official Tass news agency, "The most serious attention should be paid to high-profile crimes, including those having political motives."
No one has been arrested in connection with Nemtsov's death, though Russia's Federal Security Service chief Alexander Bortnikov did say there are suspects, Tass reported. The same agency, citing Russia's Finance Ministry, said that investigators are looking for a car that belongs to a state enterprise that provides services to that ministry.
Putin didn't identify any person or group that might be directly responsible.
But Wednesday he took the opportunity to lay blame generally at what he called "color technologies," an apparent reference to using mass street protests and overseas funding to try to overthrow a government.
"The actions of extremists are becoming more and more widespread," the President said
. "We are running into attempts of using so-called color technologies, from organizing illegal street protests to open propaganda (expressing) hatred in social networks."