Western leaders have called on the Russian authorities to get to thetruth behind the killing of opposition politician Boris Nemtsov.
The US president urged a "transparent investigation". The German chancellor said the killing must be explained and the perpetrators brought to justice.
Mr Nemtsov was shot four times in the back on a bridge near the Kremlin.
President Vladimir Putin condemned the killing, saying he had taken personal control of the investigation.
In a telegram to Mr Nemtsov's mother, posted on the Kremlin's website, Mr Putin said: "Everything will be done so that the organisers and perpetrators of a vile and cynical murder are punished."
He offered his "deepest condolences on the irreparable loss" and praised Mr Nemtsov, saying he "left his mark on the history of Russia" and "always openly and honestly stated his position and defended his point of view".
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.
It added that the attack was meticulously planned and the killers - who fled in a car - had been tracking Mr Nemtsov's movements around the city.
Boris Nemtsov died hours after appealing for support for a march on Sunday in Moscow against the war in Ukraine.
The march, due to be held in a Moscow suburb, has now been cancelled, and the organisers have been given permission to hold a mourning procession in the centre of the city.
Russian state TV said it would begin on Kitaigorodsky Proezd at 15:00 local time (12:00 GMT). Analysts say it is rare for state media to announce the time and place of opposition rallies.
'Bridge destroyed' Amid widespread global outrage, US President Barack Obama condemned the killing of Mr Nemtsov as a "brutal murder".
The Russian government must conduct a "prompt, impartial and transparent investigation", the US president 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," Mr Obama said in a statement.