Ilya Yashin, a close associate of Nemtsov, said the killing was a political murder as Nemtsov had been preparing a report on the war in eastern Ukraine with evidence showing that Russian soldiers are fighting there, a fact still denied by Moscow.
According to his spokesman, Mr Putin said "this brutal murder has all the hallmarks of a contract killing and is a pure provocation". Dmitry Peskov added that the president had taken the investigation into the murder under his personal responsibility.
Opposition members said Mr Putin's move to brand the killing as a provocation bode ill for his critics. "This sounds as if he is accusing us of staging this," said a member of the staff of Alexei Navalny, the opposition leader and anti-corruption blogger. "They might use this as a pretext to move against us ahead of the rally."
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The opposition is planning a march, the leaders of which hope will attract more than 10,000 people on Sunday to protest against the economic crisis in the country and Mr Putin's involvement in the war in Ukraine. However, there was a suggestion that the march could be changed into a mourning event instead.
"Of all the politicians, Boris Nemtsov was the most human one," tweeted Vladimir Ashurkov, an associate of Mr Navalny who went into exile last October. "Kind and sympathetic. Fond memories . . ."
At 2am, people started coming to lay flowers at the crime scene.
In an interview with the FT on Monday night, Nemtsov said now was "an absolute low point" for Russia's opposition, which since the 2012 protests had been shattered and needed to get on its feet again. He said that under Mr Putin's clampdown on opposition activists, the media and civic groups, the president's critics had become no more than dissidents, and the most important task now was to rebuild a real opposition.
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He also expressed pessimism over the prospects for political change. To replace Mr Putin could potentially take until 2024, the end of another six-year term after the current one ends in 2018.
Nemtsov said he intended to work towards this goal by convincing Russians that Mr Putin was to blame for the country's economic decline and that Russia was waging a war in Ukraine. "The war could become an important force for change because if they continue fighting, more and more military families will know, and Putin's support in the military and in the security services will crumble," he said.
A scientist who held degrees in physics and mathematics, Nemtsov's political career reached back into the final years of the Soviet Union when he organised a protest after the nuclear disaster in Chernobyl and in 1990 was elected as a parliamentary deputy for the first time.
During the 1990s, he held positions as a regional governor, a member of the upper house in parliament and in the government of Mr Putin's predecessor Boris Yeltsin.
An avowed liberal, Nemtsov had been campaigning against Mr Putin since his first term as president.
Nemtsov was one of the leaders of the protests against Mr Putin which brought more than 100,000 people to the streets of Moscow in late 2011 and early 2012.
In a statement on Twitter, President Barack Obama said that the "United States condemns the brutal murder of Boris Nemtsov." He called on the Russian government to conduct "a prompt, impartial and transparent investigation and to ensure those responsible are brought to justice".
US secretary of state John Kerry said: "Boris Nemtsov committed his life to a more democratic, prosperous, open Russia, and to strong relationships between Russia and its neighbours and partners, including the United States.
"His absence will be deeply felt in Russia and around the world. The United States urges the Russian authorities to act expeditiously to investigate and bring to justice those responsible."
Leading Republicans in Congress urged the Obama administration to give more support to the opposition in Russia.
"Lawlessness now pervades Putin's Russia," said Ed Royce, chairman of the House foreign affairs committee. "Regardless of who killed Boris Nemtsov, this shocking murder is the latest assault on those who dare to oppose the Putin regime."
The murder of Nemtsov comes as the White House is debating whether to provide heavy weapons to Ukraine to fight back against Russia-backed rebels — a proposal that already has strong support in Congress.