Reuters could not independently verify the handcuffed man's assertions and there was no immediate comment from Ukraine.
The Kommersant newspaper reported on Wednesday that a car bomb had injured an officer from Russia's military intelligence agency in northern Moscow.
Other media said the injured man was a regular military officer.
Russia's interior ministry said at the time that two people had been injured in the blast and a criminal case had been opened.
CCTV footage showed a Toyota LandCruiser parked outside what looked like a residential complex exploding into a fireball.
Turkish authorities said late on Wednesday they had arrested a Russian citizen suspected of the attack in Bodrum after he had flown in from Moscow.
On Friday, Russia's FSB security service said the man, whom it named as Yevgeny Serebyrakov, had been brought to Russia from Turkey and handed over to investigators.
In a video released by RIA, which had been edited in places to remove certain references, Serebyrakov said he had been recruited by Ukrainian intelligence in 2023 and asked to kill "an officer".
He says in the video he gathered the components to make a homemade bomb at his Ukrainian handler's request and placed it beneath the unnamed officer's vehicle.
He was promised Ukrainian citizenship and $US10,000-$US20,000 ($A15,000-$A30,000) as a reward for his work, he said.
