he was walking with a woman along a bridge just metres from the Kremlin.
The Life News website identified the woman as 23-year-old Ukrainian model.
One or more gunmen shot at Nemtsov at least seven or eight times, investigators said. They said one of the weapons was believed to be a Makarov pistol, used by Russian military and police.
Cartridges left at the scene came from different manufacturers, making them harder to trace, they said.
The killers evidently knew Nemtsov was planning to walk to his flat nearby, they added.
They said initial hypotheses included a link to “Islamist extremism” and the Charlie Hebdo massacre, noting that Nemtsov had received threats after he condemned the killings in Paris as well as “situation inside Ukraine”.
Speaking on radio just hours before his murder, Nemtsov sounded upbeat and urged Russians to join the planned opposition rally on Sunday.
“The key political demand is an immediate end to the Ukraine war,” he said on popular Echo of Moscow radio, adding that Putin should quit.
The current regime has reached “a dead end in both domestic and foreign policies. They should go,” Nemtsov said.
The former researcher rose to prominence as governor of the Nizhny Novgorod region in central Russia and became a vice prime minister in the late 1990s under the presidency of Boris Yeltsin.
After leaving parliament in 2003, he led several opposition parties and groups.
A passionate orator with a rock star image and popular with women, Nemtsov was a key speaker at mass opposition rallies against Putin’s return to the Kremlin in 2012.
He wrote a series of reports critical of corruption and misspending under Putin.
In 2013, he said up to $30 billion of the estimated $50 billion assigned to the Olympic Games that Russia was to host in Sochi had gone missing. The Kremlin has denied the claims.
“This is payback for the fact that Boris consistently, for many, many years fought for Russia to be a free democratic country,” opposition leader Mikhail Kasyanov, who served as prime minister under Putin, told reporters after visiting the murder scene. “In the 21st century, in 2015, a leader of the opposition is shot dead by the Kremlin walls. It is beyond imagination.”
Washington led condemnation of the killing.
“We call upon the Russian government to conduct a prompt, impartial and transparent investigation into the circumstances of his murder and ensure that those responsible for this vicious killing are brought to justice,” Obama said in a statement.
Ukrainian President Petro Poroshenko called Nemtsov a “bridge between Ukraine and Russia”.
“The murderers’ shot has destroyed it. I think it is not by accident.”
A steady stream of people heaped flowers and photos of Nemtsov and set candles at the site of the murder on Saturday, with police closing off one lane of traffic to let them through.
Opposition activists have now scrapped the rally, while the authorities have permitted a march in memory of Nemtsov through the city centre.
“We are in a new political reality,” said one of the organisers, Leonid Volkov.
Alexei Venediktov, editor-in-chief of Echo of Moscow radio, wrote that Nemtsov, who leaves behind four children and an elderly mother, knew he was taking risks by openly criticising Putin. “But I will not leave Russia, who would fight then?” he quoted the veteran politician as saying.