Families, the old and young walked slowly, with many carrying portraits of Nemtsov, an opposition politician and former deputy prime minister who was shot dead while walking home from a restaurant in central Moscow on Friday night.
"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," Gennady Gudkov, an opposition leader, told Reuters before the march.
"The authorities are corrupt and don't allow any threats to them to emerge. Boris was uncomfortable for them."
His murder has prompted deep soul searching in a country where for years after the Soviet Union collapsed many yearned for the stability later brought by President Vladimir Putin. Some now fear his rule has become an autocracy.
Putin has vowed to pursue those who killed Nemtsov, calling the murder a "provocation".
National investigators who answer to the Russian leader say they are pursuing several lines of inquiry, including the possibility that Nemtsov, a Jew, was killed by radical Islamists or that the opposition killed him to blacken Putin's name.
Putin's opponents say such suggestions show the cynicism of Russia's leaders as they whip up nationalism, hatred and anti-Western hysteria to rally support for his policies on Ukraine and deflect blame for an economic crisis.
"It is a blow to Russia. If political views are punished this way, then this country simply has no future," Sergei Mitrokhin, an opposition leader, said of Nemtsov's murder.
Some Muscovites, accepting a line repeated by state media, appear to agree that the opposition, struggling to make an impact after a clampdown on dissent in Putin's third spell as president, might have killed one of their own.
"The authorities definitely do not benefit from this. Everybody had long forgotten about this man, Nemtsov ... It is definitely a 'provocation'," said one Moscow resident, who gave his name only as Denis.
Some young people walking in central Moscow asked: "Who is Nemtsov anyway?"
PUTIN REMAINS DOMINANT
Nemtsov, who was 55, was one of the leading lights of an opposition struggling to revive its fortunes, three years after mass rallies against Putin that failed to prevent him returning to the presidency after four years as prime minister.
The opposition has little support outside big cities and Putin has now been Russia's dominant leader since 2000, when ailing President Boris Yeltsin chose the former KGB spy as his successor, a role Nemtsov had once been destined to play.
Even many of Putin's opponents have little doubt that he will win another six years in power at the next election, due in 2018, despite a financial crisis aggravated by Western economic sanctions over the Ukraine crisis and a fall in oil prices.
Many opposition leaders have been jailed on what they say are trumped-up charges, or have fled the country. Their most prominent leader, Alexei Navalny, is serving a 15-day jail sentence for breaking a law that restricts demonstrations.
Nemtsov, a fighter against corruption who said he feared Putin may want him dead, had hoped to start the opposition's revival with a march in Marino on the outskirts of Moscow to protest against Putin's economic policies and what they see as Russia's involvement in the separatist war in east Ukraine.
The Kremlin denies any role in the fighting.
In a change of plan, the opposition said Moscow city authorities had allowed a march of up to 50,000 people alongside the River Moskva to commemorate Nemtsov's death.
Ukrainian President Petro Poroshenko said Nemtsov had told him about two weeks ago that he planned to publish evidence of Russian involvement in Ukraine's separatist conflict.