Kiev had said the 41-year-old Russian journalist, a strong critic of President Vladimir Putin, was shot multiple times in the back at his apartment building while on his way to buy bread on Tuesday night.
Moscow said it was happy that Mr Babchenko was alive after all.
Agency Chief Vasily Gritsak said the killing was ordered by "Russian special services" and there was "indisputable evidence of the terrorist activity of Russian special forces in Ukraine".
"I'm sorry, but there were no other options". He apologized to her "for the hell she had to go through in the past two days".
Police in Kiev had said on Tuesday that Babchenko's supposed death had most likely been due to his work as a journalist.
To the amazement and applause of the assembled journalists at the headquarters of the State Security Service, or SBU, Ukrainian authorities said they had staged his murder.
Mohamed Salah to Miss First World Cup Games
The competition begins June 14, and Egypt's first game falls on June 15, exactly 21 days after Salah's injury May 26. Liverpool forward Mohamed Salah will be fit to play some part in Egypt's World Cup campaign, his country says .
Friday Is National Donut Day, and You Know What That Means
Free doughnuts are limited to only the 18 classic styles, which include the Boston cream and the traditional jelly doughnut. The Philadelphia doughnut shop Factory Donuts is giving each customer not one but two free doughnuts on Friday, June 1 .
Stephen Curry Is No Fan Of People Disrespecting LeBron James' Teammates
Green performed well in replacing Love in Game 6, finishing with 14 points, three rebounds and two blocks off the bench. Love had been averaging 13.9 points per game with 10 rebounds in the postseason this year.
"I have buried many friends and colleagues many times and I know the sickening feeling", he said.
Oleg Kashin, a Russian journalist who was brutally attacked in 2010, told HuffPost UK that while the development was undoubtedly good news, those close to Babchenko might not be so pleased: "What is better- to be killed or to be part of this Macabre show?"
Babchenko, 41, fled his native Russia for Ukraine a year ago after receiving death threats for criticizing Russian military involvement in Syria.
They had claimed he was found bleeding by his wife.
"I would like to apologise for what you have all had to go through", Babchenko said.
Russia's Foreign Ministry, which had earlier denied any involvement in Babchenko's death, said it was pleased to hear that he was actually alive, accusing Ukraine of "propaganda".
Prominent Russian journalist Arkady Babchenko.
Babchenko left Russian Federation after he criticized the Kremlin in a Facebook post in 2017.
In coordination with Ukrainian police, Mr Babchenko staged his death as part of an investigation into death threats he had received.