"Everything will be done to bring the organizers and perpetrators of this cowardly and cynical murder the punishment they deserve," the president said in a statement posted on his website.
According to the Russian Interior Ministry, Nemtsov was killed at 11:40 p.m. Moscow time on Friday (20:40 GMT), when several shots were fired at him from a car.
"I sincerely share the grief that has befallen you… He has always openly and honestly stated his position and defended his point of view," the Russian president's statement read.
Vladimir Putin has sent a message of condolence to Dina Eidman, Boris Nemtsov's mother— President of Russia (@KremlinRussia_E) 28 февраля 2015
Late on Friday, Putin said that the killing had all the signs of a contract murder and was extremely provocative. He ordered Russia's Investigative Committee, Interior Ministry and Federal Security Service to set up an investigative team.
As of Saturday, the Investigative Committee's Chief Investigation Department took charge of the investigation into Nemtsov's murder. Investigators believe he had allegedly been shot from a Makarov pistol.
Several versions are currently considered, with some of them establishing a connection between the murder and the Charlie Hebdo attack in Paris, current events in Ukraine and the politician's business activity.