Mr Nemtsov was shot four times in the back late on Friday while walking on a bridge near the Kremlin with his girlfriend, Anna Durytska, 23. He died at the scene. No suspects have been arrested.
Many of his supporters suspect the killing was ordered by the Kremlin in retaliation for Mr Nemtsov’s ardent criticism of president Vladimir Putin, while authorities have suggested several possible motives, including a provocation aimed at tarnishing Mr Putin’s image.
With an hour to go until the scheduled end of the viewing, the line of mourners stretched for hundreds of metres and included mourners young and old.
Valentina Gorbatova, 80, said: “He was our ray of light. With his help, I think Russia would have risen up and become a strong country. It is the dream of all progressive people in Russia.”
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Mr Nemtsov, 55, had been a deputy prime minister under president Boris Yeltsin and was widely seen as a rising young reformer. However, in the Putin era Mr Nemtsov’s party lost its seats in parliament.
But although his influence in mainstream politics vanished, he remained visible as one of Mr Putin’s most vehement critics.
Just a few hours before his death, Mr Nemtsov conducted a radio interview in which he denounced Mr Putin for “mad, aggressive” policies in the Ukraine crisis.
The politician’s body lay in a coffin in the Sakharov Centre in central Moscow, named after the late Soviet-era dissident and Nobel Peace Prize laureate Andrei Sakharov. The funeral and burial were held later.
Among those at the viewing were US Ambassador John Tefft and former Russian prime minister Mikhail Kasyanov, who has since joined the opposition. Russian deputy prime ministers Sergei Prikhodko and Arkady Dvorkovich and Boris Yeltsin’s widow, Naina, also came.
“They probably know that if they don’t come, then at some point people will be coming for them,” Irina Khakamada, co-leader of a liberal party in parliament with Mr Nemtsov, said of the Russian government officials.
However, several European Union politicians were barred from attending the funeral.
Human rights activist Lev Ponomarev echoed the view of many opposition figures that the strong nationalism and intolerance of dissent that has risen up under Mr Putin has coarsened society and encouraged violence.
He said: “In this atmosphere of violence and hate, these killings will only continue.”
Commentators said, like other key opposition leaders, Mr Nemtsov was constantly being shadowed by police, so it would be hard to imagine that his killing could go unnoticed by them.