Vladimir Putin has said he will do everything possible to bring to justice those who committed the “vile and cynical” murder of Russian opposition leader Boris Nemtsov.

In a telegram to Boris Nemtsov’s mother, published on the Kremlin’s website, the Russian president offered condolences and praised Nemtsov’s openness and honesty.

Boris Nemtsov, 55, was shot four times in the back on a bridge near the Kremlin.

Western leaders demanded a transparent investigation into the killing.

In the telegram to Boris Nemtsov’s 86-year-old mother, Dina Eydman, Vladimir Putin said: “We will do everything to ensure that the perpetrators of this vile and cynical crime and those who stand behind them are properly punished.”

He said: “Please accept my deepest condolences in connection with this irreparable loss. I sincerely share your sorrow.

“Boris Nemtsov has left his mark in the history of Russia, in its political and public life. He occupied significant posts in a difficult time of transition in this country. He always openly and honestly voiced and upheld his views.”

Expressing shock at the “cruel and cynical murder”, PM Dmitry Medvedev said Boris Nemtsov was a “principled person” who “acted openly, consistently and never betrayed his views”.

On February 28 there was a steady stream of people leaving flowers at the site of the killing.

Boris Nemtsov served as first deputy prime minister under President Boris Yeltsin in the 1990s but fell out of favor with Vladimir Putin and became an outspoken opponent, particularly on the Ukraine conflict.

During an interview on February 10, Boris Nemtsov had said he feared Vladimir Putin would have him killed because of his opposition to the war.

Boris Nemtsov died hours after appealing for support for a march on March 1 in Moscow against the conflict.

The march, due to be held in a Moscow suburb, has now been cancelled, and the organizers have been given permission to hold a mourning procession in the centre of the city.

According to the Russian state media, the march will begin on Kitaigorodsky Proezd at 15:00 local time and pass the site of the killing. Analysts say it is rare for state media to announce the time and place of opposition rallies.

Amid widespread global outrage, President Barack Obama condemned the killing as a “brutal murder”.

The Russian government must conduct a “prompt, impartial and transparent investigation”, Barack Obama urged.

“I admired Nemtsov’s courageous dedication to the struggle against corruption in Russia and appreciated his willingness to share his candid views with me when we met in Moscow in 2009,” the president said in a statement.

A statement from the office of German Chancellor Angela Merkel spoke of Boris Nemtsov’s “courage” for his frequent criticism of Russian government policy.

Angela Merkel “calls on President Vladimir Putin to ensure that the murder is cleared up and the perpetrators brought to justice”, her spokesman Steffen Seibert said.

UK PM David Cameron echoed the calls for an inquiry, saying he was “shocked and sickened” by the news.

Ukrainian President Petro Poroshenko described Boris Nemtsov as a friend of Ukraine.

He said: “Boris had declared he would provide clear evidence of Russian armed forces’ participation in [the war] in Ukraine. Somebody was afraid of this… They killed him.”

Amnesty International demanded a “prompt, impartial and effective” investigation into what it said was “a cold-blooded murder of one of those free voices whom the authorities have so actively sought to silence”.

Boris Nemtsov was shot at around 23:40 on Friday, February 27, while crossing Bolshoy Moskvoretsky Bridge accompanied by a woman, Russia’s interior ministry said.

He was shot with a pistol from a white car which fled the scene, police said.

Russian investigative committee head Vladimir Markin said in a statement that several motives for the killing were being considered including “Islamic extremism” and the victim’s alleged links with Ukraine.

“Mr. Nemtsov may have been sacrificed by those who do not shun anything to reach their political gains,” the statement said.

The statement also said that the attack was meticulously planned and the killers had been tracking Boris Nemtsov’s movements around Moscow.

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