Three people were killed and about 260 wounded on April 15 last year when two bombs made of explosives-packed pressure cookers went off near the finish line of the marathon.
US authorities are seeking the death penalty for Dzhokhar Tsarnaev, then 19, for his alleged role in the blasts. His brother Tamerlan, 26, died after an exchange of fire with police after the Chechen Muslim brothers went on the run, sparking a four-day manhunt.
The Russian side said that Tamerlan "had changed drastically since 2010 as he prepared to leave the United States for travel to the country's region to join unspecified underground groups."
But, according to The Times, after an initial investigation by FBI agents in Boston, the Russians declined several requests for additional information they had about him.
More From This Section
The inspector general's report found that it was only after the bombing that the Russians shared the additional intelligence, including information from a telephone conversation the Russian authorities had intercepted between Tamerlan and his mother in which they discussed jihad, the Times said.
Dzhokhar Tsarnaev's trial begins in November.
The one-time student has pleaded not guilty to 30 federal charges related to the bombings, including 17 serious charges that can carry sentences of death or life in prison.