Jim Treacy, the FBI's legal attaché in Moscow between 2007 and 2009, said the Russians long asked for U.S. assistance regarding Chechen activity in the United States that might be related to terrorism.
"On any given day, you can get some very good cooperation," Treacy said. "The next you might find yourself totally shut out."
Zubeidat Tsarnaeva has denied that she or her sons were involved in terrorism. She has said she believed her sons have been framed by U.S. authorities.
But Ruslan Tsarni, an uncle of the Tsarnaev brothers and Zubeidat's former brother-in-law, said Saturday he believes the mother had a "big-time influence" as her elder son increasingly embraced his Muslim faith and decided to quit boxing and school.
After receiving the narrow tip from Russia in March 2011, the FBI opened a preliminary investigation into Tamerlan and his mother. But the scope was extremely limited under the FBI's internal procedures.
After a few months, they found no evidence Tamerlan or his mother were involved in terrorism.
The FBI asked Russia for more information. After hearing nothing, it closed the case in June 2011.
In fall 2011, the FSB contacted the CIA with the same information. Again the FBI asked Russia for more details and never heard back.
At that time, however, the CIA asked that Tamerlan's and his mother's name be entered into a massive U.S. terrorism database.
The CIA declined to comment Saturday.
Authorities have said they've seen no connection between the brothers and a foreign terrorist group. Dzhohkar told FBI interrogators that he and his brother were angry over wars in Afghanistan and Iraq and the deaths of Muslim civilians there.
Family members have said Tamerlan was religiously apathetic until 2008 or 2009, when he met a Muslim convert known only to the family as Misha. Misha, they said, steered Tamerlan toward a stricter version of Islam.
Two U.S. officials say investigators believe they have identified Misha. While it was not clear whether the FBI had spoken to him, the officials said they have not found a connection between Misha and the Boston attack or terrorism in general.