The FBI said that it responded by interviewing Tsarnaev and family members, but found no terrorism activity.
Both parents insist that the FBI continued to monitor Tamerlan Tsarnaev and that both of their sons were set up.
Their mother went so far on Sunday to claim that the FBI had contacted her elder son after the deadly bombs exploded at the marathon. If true, it would be the first indication that the FBI considered him a suspect before Boston descended into violence on Thursday.
The FBI declined to comment publicly Sunday.
The mother's claim could not be independently confirmed, and she has made statements in the past that appeared to show a lack of full understanding of what occurred in Boston.
Investigators released photos and video of the two Tsarnaev brothers on Thursday afternoon, but at that point their identities were not known. By late that night, Tamerlan Tsarnaev was dead.
Tsarnaeva said her elder son told her by telephone that the FBI had called to inform him that they considered him a suspect and he should come in for questioning.
She said her son refused. "I told them, what do you suspect me of?" Tsarnaeva quoted her son as saying. "This is your problem and if you need me you should come to where I am."
He then told her he was going to drive his younger brother to the university, she said, speaking by telephone from Chechnya. Tsarnaeva claimed that her son later called his wife to tell her they were being chased and fired upon.
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