A prominent Russian journalist and critic of President Vladimir Putin was shot dead in Ukraine where he had fled into exile following threats, police said on Tuesday.

Arkady Babchenko, 41, died of his wounds in an ambulance after his wife found him covered in his blood in their home, police said, adding they suspected the murder was due to Babchenko's professional activities.

Babchenko, a former soldier in the Chechen war who became one of Russia's best-known war correspondents, had left his homeland fearing for his life after criticising Russian policy in Ukraine and Syria.

He had been denounced by pro-government politicians in Russia over comments on social media about the Russian bombing of Aleppo in Syria's war, and over his characterisation of Russia as an aggressor towards Ukraine.

"The first and the most probable version is his professional activity," Kiev police chief Andriy Kryshchenko said at a televised press briefing when asked what police suspected lay behind the murder.

Babchenko's wife is in a state of shock and police are unable to speak to her, he said. Ukrainian authorities released a drawing of the man they suspect is Babchenko's assassin, around 40-45 years old, with a grey beard and wearing a cap.

Two years ago Pavel Sheremet, a Belarussian journalist known for his criticism of his home country's leadership and his friendship with the slain Russian opposition leader Boris Nemtsov, was blown up in a car bomb in central Kiev.

"Putin's regime takes aim at those who cannot be broken or intimidated," Anton Gerashchenko, a Ukrainian lawmaker and adviser to the interior minister, wrote on Facebook.

Babchenko's house had run out of bread and he had gone to the shops to buy some, Gerashchenko said. He was gunned down on Tuesday by someone waiting for him in the stairwell at the entrance to his home. He was shot him in the back several times.

"Today in Kiev on the threshold of the apartment where he lived, famous Russian journalist Arkady Babchenko was shot and killed, a consistent opponent of the Putin regime and a friend of Ukraine."

In a statement, the Russian foreign ministry said journalists were being killed with impunity in Ukraine.

"Bloody crimes and total impunity have become routine for the Kiev regime. We demand that the Ukrainian authorities make every effort to promptly investigate," it said on Facebook.

The Investigative Committee of Russia said it had opened a criminal case into Babchenko's death.

Babchenko took part in the war in Chechnya as a soldier. He then he became a war reporter for several Russian newspapers. On Feb. 27 last year, he wrote on Facebook that he had left Russia.

He reported on Russia sending private military contractors to Syria and the downing of Malaysia Airlines Flight MH-17 in July 2014 in eastern Ukraine, for which investigators last week held the Russian state responsible. Russian authorities again denied any connection with the plane's downing over an area of Ukraine held by pro-Russian separatist forces.

In his last Facebook post before he was killed, Babchenko recalled an incident four years ago when he was meant to fly in a Ukrainian military helicopter in Ukraine's embattled Donbass region. The helicopter was overloaded and he was not permitted to fly. It was shot down and 14 people on board were killed.

"And I was lucky. Second birthday, it turns out," he wrote.