Russia's top investigative body is looking into several possible motives for the killing of prominent opposition figure Boris Nemtsov, including an attempt to destabilise the state, Islamic extremism, the Ukraine conflict and his personal life.

A statement from the Investigative Committee did not address the possibility seen as likely by many of Nemtsov's supporters - that he was killed for being one of president Vladimir Putin's most adamant and visible critics.

Nemtsov, 55, was gunned down as he walked on a bridge near the Kremlin with a female companion. The killing came just a few hours after a radio interview in which he denounced Putin's "mad, aggressive" policies and the day before he was to help lead a rally protesting at Russia's actions in the Ukraine crisis and the economic crisis at home.

After his death, organisers cancelled the rally and instead called for a demonstration to mourn him on Sunday in central Moscow. The city gave quick approval for that gathering, in contrast to its usual slow and grudging permission for opposition rallies.

The Investigative Committee said it was looking in to whether Nemtsov had been killed as a "sacrificial victim for those who do not shun any method for achieving their political goals", a suggestion echoing the comments by Putin's spokesman and other Russian politicians that the attack was a "provocation" against the state.

It also said it was considering whether there was "personal enmity" toward him in his domestic life. State-controlled TV and Kremlin-friendly media outlets today gave considerable attention to the woman Nemtsov was walking with, identifying her as a Ukrainian model 30 years his junior and showing photos of her in alluring poses; the Investigative Committee said the pair were headed for Nemtsov's apartment.

The statement also said it was investigating whether the killing was connected to the Ukraine conflict, where Russia-backed separatists have been fighting Ukrainian forces since last April, or whether there was a connection to Islamic extremism.

Nemtsov had been one of Putin's most visible critics and his death hit other members of the opposition hard. The mourning march on Sunday could serve to galvanise the beleaguered and marginalised opposition, or it could prove to be a brief catharsis after which emotions dissipate.

Through the morning, hundreds of people came to the site of Nemtsov's death to lay flowers.

Nemtsov was working on a report presenting evidence that he believed proved Russia's direct involvement in the separatist rebellion that has raged in eastern Ukraine since April. Moscow denies backing the rebels with troops and sophisticated weapons.

Putin ordered Russia's top law enforcement chiefs to personally oversee the investigation of Nemtsov's killing.

"Putin noted that this cruel murder has all the makings of a contract hit and is extremely provocative," presidential spokesman Dmitry Peskov said in remarks carried by Russian news agencies.

US Secretary of State John Kerry said Nemtsov committed his life to a more democratic Russia, "and to strong relationships between Russia and its neighbours and partners, including the United States."

German chancellor Angela Merkel praised Nemtsov's courage in criticising Kremlin policies, and urged Putin to ensure that the killers are brought to justice, her spokesman Steffen Seibert said.

Former Soviet leader Mikhail Gorbachev echoed the suggestion that the killing was a provocation. "It's an attempt to push the situation into complications, maybe even to destabilising the situation in the country," he was quoted as saying by the Interfax news agency.

Communist Party leader Gennady Zyuganov agreed. "It's a provocation; for big fires, sacrificial figures are necessary," Interfax quoted him as saying.

Nemtsov frequently assailed the government's inefficiency, rampant corruption and Ukraine policy.

In an interview with the Sobesednik newspaper, Nemtsov said earlier this month that his 86-year old mother was afraid that Putin could have him killed. Asked if he had such fears himself, he responded: "If I were afraid I wouldn't have led an opposition party."

Speaking on radio just a few hours before his death, he accused Putin of plunging Russia into crisis by his "mad, aggressive and deadly policy of war against Ukraine".

Nemtsov's lawyer, Vadim Prokhorov, said the politician had received threats on social networks and told police about them, but authorities took no steps to protect him.

Interior Ministry spokeswoman Yelena Alexeyeva told reporters that Nemtsov was walking with a female acquaintance, a Ukrainian citizen, when a vehicle drove up and unidentified people shot him. The woman wasn't hurt and was being questioned by police.

Mikhail Kasyanov, the former prime minister, said he was shocked.

"In the 21st century, a leader of the opposition is being demonstratively shot just outside the walls of the Kremlin," Kasyanov told reporters as Nemtsov's body, placed in a plastic bag, was removed on a rainy and cold night, as the Kremlin bells chimed nearby. "The country is rolling in to the abyss."

"This is a monstrous tragedy and a loss for us all," Alexei Navalny, Russia's most prominent opposition figure, said on his Facebook page. He is currently on a 15-day jail sentence for handing out leaflets without authorisation.

Garry Kasparov, a former chess champion who worked with Nemtsov to organise protests against Putin and now lives in the United States, said the killing shows that Putin and those who support him are lying when they say their popular support is strong.

"If you have 86% support, why do you kill someone like Boris?" he said.

Opposition activist Ilya Yashin, who last spoke to Nemtsov two days before the killing, said he had no doubt that Nemtsov's murder was politically motivated.

"Boris Nemtsov was a stark opposition leader who criticised the most important state officials in our country, including president Vladimir Putin. As we have seen, such criticism in Russia is dangerous for one's life," Yashin said.

Nemtsov served as a regional governor and then a deputy prime minister in the 1990s and once was seen as a possible successor to Boris Yeltsin, Russia's first elected president. After Putin came to power in 2000, Nemtsov became one of his most vocal critics.

Nemtsov was widely liked for his good humour, larger-than-life character and quick wit, but he and other top opposition figures long have been purged from state television and steadily marginalised by the Kremlin.