Boris Nemtsov murder: Tens of thousands march in Moscow
Tens of thousands of people have marched through central Moscow to honour opposition politician Boris Nemtsov, who was shot dead on Friday.
They carried portraits of Mr Nemtsov and banners saying "I am not afraid".
He had been due to lead an opposition march on Sunday but his killing turned the event into a mourning rally.
Mr Nemtsov's allies have accused the Kremlin of involvement, but President Vladimir Putin condemned the murder as "vile" and vowed to find the killers.
Opposition supporters gathered at a point not far from the Kremlin before marching past the spot on Great Moskvoretsky Bridge where Mr Nemtsov was killed. Some chanted "Russia without Putin!"
Several thousand people also marched in St Petersburg.
Flags and flowers
Moscow city authorities had approved a march of up to 50,000 people there.
There has been no official figure on turnout yet, with estimates ranging from 16,000 to 70,000.
Many people carried the national flag and flowers to lay at the scene of the killing, which was already piled with tributes. A few were holding Ukrainian flags.
Some of the placards read: "He died for the future of Russia" and "They were afraid of you, Boris".
Maria Glazacheva, a 22-year-old student in Moscow who joined the march, told the BBC: "Boris was a good and honest man. Moscow is a sad place today."
At the scene: Sarah Rainsford, BBC News, Moscow
The mood was sombre as the crowd gathered. Many were carrying flowers to place at the spot where Boris Nemtsov was killed. They had placards displaying his photograph, and slogans that included a play on Mr Nemtsov's name so that it read: "Fight on!"
As the crowd turned the corner and flooded on to the embankment, they began to chant. Quietly at first, but more loudly as they approached the Kremlin: "Russia without Putin" and "Putin, leave!"
These were extraordinary scenes right at the heart of Russia's capital. The police were out in force, but the march was peaceful. Many in the crowd were carrying their national flag, with a black ribbon tied to it.
They said they wanted to show that they are patriots too. That criticising those in power does not make you an enemy of the state. People told me that - like Boris Nemtsov - they just want to see a different Russia.
Opposition politician Ilya Yashin told Associated Press the killing was "a political murder aimed at frightening the... part of the population that supported Nemtsov and did not agree with the government. I hope we won't get scared".
Another opposition figure, Gennady Gudkov, told Reuters: "If we can stop the campaign of hate that's being directed at the opposition, then we have a chance to change Russia. If not, then we face the prospect of mass civil conflict."
Pro-Kremlin activists from the group Anti-Maidan had said they would not disrupt the march.
Russia's Investigative Committee said it was looking into a number of possible motives for Mr Nemtsov's murder.
They include his opposition to the Ukraine conflict, Islamic extremism - Mr Nemtsov had Jewish ancestry although he had become Orthodox Christian - and an opposition "sacrifice" of its leader to destabilise the state and undermine the president.
Presidential spokesman Dmitry Peskov said Mr Putin had noted "that this cruel murder has all the makings of a contract hit and is extremely provocative".
The investigators offered a reward of three million roubles ($48,000) for information leading to the killers.
Mr Yashin confirmed that Mr Nemtsov was preparing documents on Russian military involvement in Ukraine before his death.
Mr Yashin said: "For him the conflict between Ukraine and Russia was a real personal tragedy and he was trying to find any way to stop it. And he was trying to find proof that Mr Putin is sending our troops to Ukraine."
Mr Nemtsov, 55, had been dining at a restaurant with his girlfriend Anna Duritskaya on Friday night.
They left together to walk to his flat, crossing the bridge, where a white car drew up and Mr Nemtsov was shot four times with a pistol at around 23:40 (20:40 GMT).
Ms Duritskaya has expressed a desire to return to her home country, Ukraine, but her lawyer said her movement had been restricted. Officials said she could be subject to "additional investigative action".
In a telegram to Mr Nemtsov's mother, published on the Kremlin website, Mr Putin vowed to bring the killers to justice. He praised Mr Nemtsov's openness and honesty.
Mr Nemtsov served as first deputy prime minister under President Boris Yeltsin in the 1990s but fell out of favour with Mr Putin and became an outspoken opponent.
Violent deaths of Putin opponents
April 2003 - Liberal politician Sergey Yushenkov assassinated near his Moscow home
July 2003 - Investigative journalist Yuri Shchekochikhin died after 16-day mysterious illness
July 2004 - Forbes magazine Russian editor Paul Klebnikov shot from moving car on Moscow street, died later in hospital
October 2006 - Investigative journalist Anna Politkovskaya shot dead outside her Moscow apartment
November 2006 - Former Russian spy Alexander Litvinenko died nearly three weeks after drinking tea laced with polonium in London hotel
March 2013 -Boris Berezovsky, former Kremlin power broker turned Putin critic, found dead in his UK home