Mr Babchenko told the news conference he'd previously fled Russian Federation after receiving death threats.
His murder had been ordered by Russian security services, the head of Ukraine's security service had earlier claimed.
An unidentified gunman shot dead a prominent Russian journalist in Ukraine on Tuesday, likely for his professional activities, the Kiev police said.
Harlem Desir, the media freedom representative at the Organization for Security and Co-operation in Europe, said he was "horrified" by Babchenko's death. He left Russian Federation in February 2017, saying he was receiving threats and concerned he might be jailed.
He said: "Four years ago General Kulchitsky wouldn't take me on his helicopter because there wasn't the space".
"I want to say sorry for what you felt".
Kremlin critic Arkady Babchenko has been seen in Ukraine.
A former soldier in the Chechen war, Babchenko became one of Russia's best-known war correspondents.
Kiev and national police had reported Mr Babchenko, a strong critic of the Kremlin, was shot multiple times in the back at his apartment building and found bleeding by his wife.
The news quickly spread around the world and appeared, for the moment at least, to worsen the already strained relationship between Moscow and Kiev.
His reported murder had triggered a war of words between Ukraine and Russian Federation and sent shivers through the journalistic communities in both countries. They said that one arrest had been made so far.
In recent years, he became increasingly alienated from Moscow journalists critical of the Kremlin.
Babchenko told RFE/RL in December 2016 that "all of the elements" of Russia's state "propaganda machine" were engaged against him after he posted comments to Facebook about the crash of a Russian military plane in the Black Sea.
Ukraine had released an image of a man wanted in connection with the killing.
He moved to Kyiv last fall, where he worked as a host for the Crimean Tatar TV station, ATR.