Moscow (CNN) This was supposed to be a rally led by Boris Nemtsov, had he lived two more days to see it.

But after the Russian opposition figure was gunned down Friday night, Sunday's rally in Moscow took on a different theme. Instead of gathering to criticize Russia's policies on Ukraine, thousands of people came together to mourn the death of the former deputy prime minister.

And as they united near the site of Nemtsov's death, conspiracy theories swirled over who killed the staunch critic of President Vladimir Putin as he walked near the Kremlin with his Ukrainian model companion.

Ukrainian President Petro Poroshenko added fuel to the conspiracists' fire by saying Saturday that Nemtsov was about to reveal information that would be damaging to Russian interests, according to Ukrinform, the state-run news agency.

"A few weeks ago I had a conversation with him on how to build relations between Ukraine and Russia, as we would like them to be. Boris said that he was going to make public the strong evidence for participation of the Russian armed forces in Ukraine. Someone was very afraid of that. Boris was not afraid, the executioners were afraid. They killed him," Ukrinform quoted Poroshenko as saying

An about-face

Russian authorities originally declined to issue a permit for the march when it was billed as an opposition rally. But they agreed to allow the procession honoring Nemtsov, said People's Freedom Party leader Mikhail Kasyanov. Nemtsov was a top official in the party.

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The 55-year-old was walking home from dinner with a companion, 23-year-old Anna Duritskaya, when he was killed. The model later called Ilya Yashin, a friend and political colleague of Nemtsov's, and said several men had pulled up in a car, and one opened fire, Yashin said.

Russian TV station LifeNews spoke with a snowplow driver, who witnessed the immediate aftermath of the slaying. He was identified as "Sergey B."

"I got on the bridge, looked into the rear mirror and saw a man on the ground. I immediately realized he didn't feel well. I drove a little bit further and pulled over," the driver said. "I realized we needed to call the ambulance and police."

In a statement on its website, the Investigative Committee for the Russian Federation said the shooter likely used a Russian-made Makarov pistol and 9 mm shells were collected at the scene.

Police say they are looking for a man with short hair who stands between 5-foot-7 and 5-foot-9, Russia's Sputnik news agency reported . The shooter was wearing blue jeans and a brown sweater.

Several possible motives were being investigated, the committee said, including the prospect that the shooting was a "provocation to destabilize the political situation in the country." The committee is also exploring the possibility that the killing is related to the Charlie Hebdo terror attack in Paris or Nemtsov's business activities, it said.

The committee is offering a reward of 3 million rubles ($49,000) for information about the crime, several media outlets reported.

Investigators interviewed Duritskaya, who was not wounded. She was reportedly being kept under guard at an apartment, and Ukraine's Foreign Ministry has requested that Duritskaya be allowed to return to Ukraine , according to TASS, a Russian news agency.

Searching for the killer

Putin quickly condemned the killing and ordered three law enforcement agencies to investigate the shooting, the Kremlin said in a statement.

The President also wrote to Nemtsov's mother saying he shared her grief and promised to bring those behind the killing to justice, the Kremlin said.

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But some of Nemtsov's fellow critics suspect involvement by either Putin's administration or a supporter of the President.

"It's clearly a political murder. It's definitely a contract one," Yashin said. "I don't know who killed Boris, but I know that it's the government and personally Putin who are responsible for it. They've been constantly promoting a hatred towards everyone who doesn't support their course and thinks different."

Putin had a different theory: that the killing was a contract hit, but one meant to fire up political strife, Putin's spokesman Dmitry Peskov said.

Nemtsov himself had said he was at risk for assassination. He told the Russian newspaper Sobesednik last month that he was "a little bit" afraid his mother's fears Putin would have him killed would come true.

But, he added, "I'm not afraid of him that much. If I was afraid I wouldn't be heading an opposition party and do what I'm doing."

Last year, Nemtsov spoke to CNN's Anthony Bourdain.

"I'm (a) well-known guy, and this is a safety because if something happens with me, it will be scandal not only in Moscow city but throughout the world," he said then.

Consequences for criticism

Critics of Putin have in the past suffered miserable fates.

Last year, a Moscow court sentenced five men to prison for the 2006 killing of Russian journalist and fierce Kremlin critic Anna Politkovskaya.

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Business magnate Mikhail Khodorkovsky accused Putin of corruption and spent 10 years in prison and labor camps.

Russian spy Alexander Litvinenko accused state security services of organizing a coup to put Putin in power. He was poisoned by a lethal dose of radioactive polonium and died in London in 2006. No killer has been caught.

And before his death, Nemtsov had been arrested several times for speaking against Putin's government.

The most recent arrests were in 2011, when he protested the results of parliamentary elections, and in 2012, when tens of thousands protested against Putin.

While Nemtsov certainly had his share of enemies in Russia -- especially those who disagree with his stance on the Ukrainian conflict -- many left notes for the slain politician on the bridge where he was killed.

"To Boris Nemtsov," one letter read, "Thank you for your example of courage and honesty."

Human rights activists did not mince words in assigning blame for Nemtsov's murder. Tweeted Garry Kasparov , chairman of the Human Rights Foundation's International Council: "If you are popular your critics don't have to be shot down in front of the Kremlin. Putin is just food in a prison, eat it or starve."

In a column on how Nemtsov had been harassed for his regular criticism of the Kremlin, Human Rights Watch's Tanya Cooper lambasted Peskov, the Putin spokesman, for saying the killing appeared to be an attempt to destabilize Russia -- a statement Cooper said could prejudice the investigation.

"Russia has become the kind of place where a top opposition leader can be murdered just steps away from the president's office," she wrote. "A country in which people are told to hate one another for difference of opinions is a dangerous country to live in."