As the agency was accused of "dropping the ball" over the case, NBC News reported that Tamerlan Tsarnaev had been seen making six visits to a known Islamic militant in a mosque in the Russian republic of Dagestan.
The visits came during a six month trip that Tamerlan made to the city of Makhachkala to see his family, NBC said.
According to a local police official, a case file on Tsarnaev was then handed over to the FBI along with a request for further information. However, the FBI never replied.
The agency has already admitted that it interviewed Tamerlan Tsarnaev in 2011 after Russia raised concerns that he was becoming a follower of radical Islam, but found nothing "derogatory" against him and did not pursue the case further.
The 26-year-old, who allegedly orchestrated last Monday's bombings with his younger brother Dzhokhar, was killed in the early hours of Friday morning in a shoot-out with police. It came just hours after police released images of the pair to the public.
In a further twist, Channel 4 News claimed on Sunday that Tamerlan had phoned home in the wake of the bombings and told his mother that the FBI had already called him to accuse him of being responsible.
According to the report, Tamerlan telephoned his mother on Wednesday last week and said he had replied to the FBI's accusations by saying: "That's your problem." The claims emerged from an interview with his father, Ansor.
The FBI declined to comment directly on either claim on Sunday.
However, if either is confirmed, they will add significant weight to the growing chorus of criticism of the FBI, which came on Sunday from senior members of Congress who accused the Bureau of repeatedly "dropping the ball".
Michael McCaul, the chair of House Homeland Security Committee, said the FBI must explain why it failed to keep track of Tsarnaev after the 2011 interview, particularly after he visited his family in Dagestan, which is a known centre of Islamist militancy and training facilities.
"If he [Tamerlan Tsarnaev] was on the radar and they let him go, if he was on the Russians' radar, why wasn't a flag put on him, some sort of customs flag?" Mr McCaul asked on CNN, adding that there were clear signs that Tsarnaev had been radicalised during his trip.
"One of the first things he does [upon his return] is puts up a YouTube website throwing out a lot of jihadist rhetoric. Clearly something happened, in my judgment, in that six-month timeframe – he radicalised at some point in time," Mr McCaul added. "Where was that and how did that happen?"
In a further sign that Tsarnaev's record was in the US security apparatus, the New York Times reported that a "hold" had been placed on his citizenship request by the Department of Homeland Security after routine background checks discovered the FBI's former interest in him.
The FBI has also not explained why it did not immediately retrieve the Tsarnaev file after the bombs exploded on Monday afternoon – an event which should have triggered routine checks on those suspected of involvement in with Islamist militant groups.
Even three days later, when the FBI correctly identified the bombers after reviewing hours of the CCTV footage and public smartphone videos of the race, they failed to cross-reference the photograph with a man whose picture they already had on file.
When contacted by The Daily Telegraph to ask why Tamerlan's file had been overlooked in the aftermath of the bombings, the FBI said it would not comment on "operational matters".
While at pains to praise the bravery of police in the hunt for the bombers, which ended last Friday night with Tamerlan, 26, dead and his younger brother Dzhokhar, 19, in hospital in a 'serious' condition, senior politicians openly questioned the competence of the FBI.
"The ball was dropped in one of two ways," said senator Lindsey Graham on CNN warning that the FBI needed to improve its performance. "The FBI missed a lot of things, is one potential answer, or our laws do not allow the FBI to follow up in a sound solid way."
"It's people like this that you don't want to let out of your sight, and this was a mistake," he added. "Either our laws are insufficient or the FBI failed, but we're at war with radical Islamists and we need to up our game."
Another Republican, congressman Peter King, chairman of the House sub-committee on Counterterrorism and Intelligence, was even more direct, accusing the FBI of having a track-record of failure in monitoring potential terror threats.
"This is at least the fifth case I'm aware of where the FBI has failed to stop someone," Mr King told Fox News, citing cases including that of Anwar al-Awlaki, who planned terrorist attacks as part of al Qaeda and Nidal Malik Hasan, who opened fire at Fort Hood, Texas, in 2009 killing 13 people.
"This is the latest in a series of cases like this...where the FBI is given information about someone as being a potential terrorist; they look at them, and then they don't take action, and then they go out and commit murders."