Nemtsov, a 55-year-old former deputy prime minister and leading Russian liberal political figure for the past two decades, was gunned down shortly before midnight Friday as he walked across a bridge near the Kremlin with a female companion.
The killing came just hours after a radio interview in which he called on Moscow residents to join an opposition rally on Sunday to protest Putin's handling of the economic crisis and his "mad, aggressive and deadly policy of war against Ukraine."
After his death, organizers canceled the rally and instead called for a demonstration to mourn him on Sunday in central Moscow. The city gave quick approval, in contrast to its usual slow and grudging permission for opposition rallies.
The mourning march could serve to galvanize the beleaguered and marginalized opposition, or it could prove to be a brief catharsis after which emotions dissipate. Popular support for Putin has remained above 80 percent in recent months, despite the severe economic recession and soaring inflation.
Russia's leading investigative agency said it was looking into several possible motives for the killing.
The first possibility, the Investigative Committee said, was that the murder was aimed at destabilizing the political situation in the country and Nemtsov was a "sacrificial victim for those who do not shun any method for achieving their political goals."
This suggestion echoed comments by Putin's spokesman and other Russian politicians that the attack was a "provocation" against the state.
The term "sacrificial victim" was also the same one Putin used three years ago when he warned that his political opponents were planning to kill one of their own and then blame it on his government.
The investigators said they also were considering whether there was "personal enmity" toward Nemtsov in his domestic life. State-controlled and Kremlin-friendly TV gave considerable attention to Nemtsov's companion, identifying her as a Ukrainian model 30 years his junior and showing photos of her in alluring poses. The Investigative Committee said the pair was headed for Nemtsov's apartment.
The agency also listed the possibility that the killing was carried out by Islamic extremists angered by Nemtsov's position on the Charlie Hebdo attack in Paris or was connected to the Ukraine conflict, where Russia-backed separatists have been fighting Ukrainian forces since last April.
Nemtsov was working on a report presenting evidence that he believed proved Russia was directly involved in the Ukraine conflict, despite official denials that it has supplied the separatists with troops and sophisticated weapons.
In a previous report on corruption released before the 2014 Winter Olympics in Sochi, Nemtsov alleged that Russian officials and businessmen had stolen up to $30 billion during the preparations for the games. He also has exposed alleged corruption in state gas company Gazprom.
Nemtsov served as a regional governor and then a deputy prime minister in the 1990s and once was seen as a possible successor to Boris Yeltsin, Russia's first elected president. But Yeltsin chose Putin instead.
Nemtsov then served a term in Russia's parliament, until all opposition parties were driven out as Putin consolidated his power. He and other leading opposition figures long have been purged by state television and steadily marginalized by the Kremlin.
In recent years, Nemtsov has been identified by Kremlin propaganda as among the leaders of a "fifth column," painted as a traitor serving the interests of a hostile West.
His death was a blow to other opposition figures, who blamed the Kremlin for creating an atmosphere of hatred and intolerance of dissent that made such a killing possible.
"For more than a year now, the television screens have been flowing with pure hate for us," Mikhail Khodorkovsky, the exiled former oil tycoon who spent a decade in prison after challenging Putin, wrote on his website. "And now everyone, from the average blogger to President Putin, is searching for enemies and accusing one another of provocation."
Through the day, hundreds of people came to the site of Nemtsov's death to lay flowers, among them the ambassadors of the U.S. and many European countries.
Putin ordered Russia's law enforcement chiefs personally to oversee the investigation of Nemtsov's killing.
He also sent a telegram to Nemtsov's 86-year-old mother, promising that "everything will be done so that the organizers and perpetrators of the vile and cynical murder get the punishment they deserve," the Kremlin said.
Presidential spokesman Dmitry Peskov earlier said Putin saw the murder as "extremely provocative."
Ramzan Kadyrov, the Putin-backed leader of Chechnya, raised the suggestion into an accusation. "There's no doubt that Nemtsov's killing was organized by Western special services, trying by any means to create internal conflict in Russia," he said on Instagram.
On a political talk show on Channel One state television Saturday night, the discussion was framed around the question of "who benefits" from Nemtsov's killing, with the accepted conclusion that it serves only Russia's enemies.
Sergei Markov, a prominent Kremlin-connected political scientist, said he suspected Ukraine's special services of carrying out the attack with the aim of splitting Russian society and bringing a more Western-friendly government to power. He added that Nemtsov was too well regarded by the Americans for them to have had him killed.
President Barack Obama said the Russian people have "lost one of the most dedicated and eloquent defenders of their rights."
German Chancellor Angela Merkel praised Nemtsov's courage in criticizing Kremlin policies, and urged Putin to insure that the killers are brought to justice, her spokesman Steffen Seibert said.
Former Soviet leader Mikhail Gorbachev echoed the suggestion that the killing was a provocation. "It's an attempt to push the situation into complications, maybe even to destabilizing the situation in the country," he was quoted as saying by the Interfax news agency.
Communist Party leader Gennady Zyuganov agreed. "It's a provocation; for big fires, sacrificial figures are necessary," Interfax quoted him as saying.
"This is a monstrous tragedy and a loss for us all," Alexei Navalny, Russia's most prominent opposition figure, said on his Facebook page. He is serving a 15-day jail sentence for handing out leaflets on the subway urging people to join Sunday's protest.
Associated Press writers Jim Heintz, Vladimir Isachenkov and Laura Mills contributed to this report.
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