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Ivan Sekretarev, Associated Press
People lay flowers at Boris Nemtsov's grave after a burial ceremony at Troekurovskoye cemetery in Moscow, Russia, Tuesday, March 3, 2015. One by one, thousands of mourners and dignitaries filed past the white-lined coffin of slain Kremlin critic Boris Nemtsov on Tuesday, many offering flowers as they paid their last respects to one of the most prominent figures of Russia's beleaguered opposition.

MOSCOW — President Vladimir Putin on Wednesday called the slaying of his top critic a "disgrace" to Russia, while the opposition promised to complete Boris Nemtsov's work on a report documenting evidence of Russian troops' involvement in fighting in eastern Ukraine.

Putin condemned the slaying of Nemtsov, who was gunned down while walking on a bridge next to the Kremlin late Friday.

The Russian leader had sent his condolences to Nemtsov's mother, but his comments Wednesday were his first public remarks on the subject.

"The most serious attention must be paid to high-profile crimes, including those with a political motive," Putin said in televised remarks to top officials of the Interior Ministry. "We must finally rid Russia of the disgrace and tragedy of the kinds of things we recently saw and experienced: I mean the audacious murder of Boris Nemtsov in the very center of the capital."

Nemtsov, 55, one of Putin's most vehement critics, was killed just hours after a radio interview in which he denounced the president for his "mad, aggressive" policies in Ukraine. Before his death, he was working on a report about Russian involvement in the war in eastern Ukraine.

Opposition activist Ilya Yashin said police had seized computers and documents during searches in Nemtsov's apartment in Moscow and his office in Yaroslavl, where he worked as a regional lawmaker.

But Yashin told The Associated Press that he and other Nemtsov's friends have found some fragments related to the report and hope to work on them and publish a report.

"He has kept his materials in different places, including with his associates and friends, and we have managed to get access to some of them," Yashin said. "We will try to restore bits and pieces of the work that Boris has started but failed to complete, and we will do everything to bring this work to the end, so that the report will see the light. It's very important for us."

On his Facebook page, Yashin posted a picture of what he said was Nemtsov's handwritten note, saying he was contacted by paratroopers from a unit that lost 17 men but who were afraid to speak publicly on the issue.

Ukraine and the West have accused Moscow of backing the pro-Russia rebellion in eastern Ukraine with troops and weapons — accusations the Kremlin has denied even though NATO said it had satellite pictures proving Russia's involvement.

No suspects have been detained yet in the killing, despite an offer of 3 million rubles (nearly $50,000) for information related to the case.

Putin dubbed Nemtsov's killing a "provocation," and nationwide TV networks quickly followed up, blaming Western intelligence agencies, Ukrainian agents or even the opposition.

The nation's top investigative agency also echoed Putin's comments, saying it was looking into whether Nemtsov had been a "sacrificial victim" to destabilize Russia. It said it was also investigating whether Islamic extremism, the Ukraine conflict and Nemtsov's personal life were possible motives.

Kremlin-controlled media focused heavily on a 23-year-old Ukrainian model, who was with Nemtsov when he was slain, with some suggesting their relationship could be a motive.

The woman, Anna Duritskaya, told Russian Dozhd television that Nemtsov was shot from behind, but said she hadn't seen the attacker, nor could she identify the license plate or make of the getaway car the gunman then sped away in. She was detained by Russian police for several days of questioning before she was allowed to return to her hometown of Kiev.

No suspects have been arrested. Divers searched for the gun in the muddy waters of the Moscow River under the bridge where Nemtsov was killed by four shots in the back.

The area is always packed with uniformed and plainclothes agents and security cameras, leading many Kremlin critics to suggest that Russia's powerful security agencies could have been involved in the assassination. They say that Nemtsov, like other prominent opposition figures, was under constant police surveillance, making official involvement even more likely.

Some observers said that certain hawkish members of Putin's entourage could have played a hand, reckoning that the assassination would further strain Russia's ties with the West, dissuade Putin from negotiating a compromise on Ukraine and take an even more isolationist course.

Asked about any possible suspects in Nemtsov's killing, Alexander Bortnikov, the head of the Federal Security Service, the main KGB successor, told Russian news agencies that "there are always suspects." He didn't elaborate.