A suspect in the shooting is wounded and has been taken to a hospital, Kiev police chief Andriy Krischenko said.
Mr. Peskov, the Kremlin spokesman, said he hoped Ukrainian authorities would solve the crime, and added that Voronenkov's widow was welcome to return to Russian Federation.
Ukrainian President Petro Poroshenko on Thursday said Voronenkov's murder "clearly shows the handwriting of Russian special services shown repeatedly in various European capitals in the past".
"We think that all the fabrications that can already be heard about a "notorious Russian link" are absurd", said Kremlin spokesman Dmitry Peskov.
The assailant also wounded Voronenkov's bodyguard, who fired back and wounded the gunman.
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A former Communist Party member in the Russian Dumas parliament, he fled the country fearing for his safety after speaking out against Putin.
Voronenkov was providing testimony in a treason case against ex-Ukrainian President Viktor Yanukovych, who was toppled in deadly protests three years ago and now lives in Russian Federation.
Voronenkov, who moved to Ukraine previous year and had criticized the Russian government, was shot dead in central Kyiv on March 23.
Lutsenko said investigators were looking into Voronenkov's role in exposing a contraband ring in Russian Federation which cost several senior security officers their jobs, and also his testimony on Yanukovych as possible motives behind his killing. This month, a Moscow court ordered the arrest in absentia of the former deputy.
The Kremlin has confirmed that President Vladimir Putin has been informed of the murder but refused further comments.
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Following his failure to win a seat in Russian parliament during last year's elections, Voronenkov emigrated to Ukraine with his family and issued several lines of criticism against the government of his native country. Thus, he chose to go to Ukraine, where he made statements against his country, although in recent times, he seemed to have plans to return to Russian Federation.
Moscow and Kiev have been locked in a bitter dispute since Russian Federation seized Crimea in March 2014, plunging ties between Moscow and the West to their lowest point since the Cold War. Both men were scheduled to give testimony later in the day at Ukraine's Military Prosecutor's Office.
Earlier, an adviser to Ukraine's interior minister, Anton Gerashchenko disclosed the name of Voronenkov's murderer.
Voronenkov, 45, had been placed on a Russian federal wanted-list in connection with an alleged $5 million property fraud. Voronenkov left Russian Federation in the autumn of 2016 because of criminal prosecution. In the same interview with Radio Free Europe in February, he called Russia's annexation of Crimea a "mistake" and likened the mood and political process in Russian Federation to Nazi Germany.
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