On Thursday, John Miller said one person is behind most of the bomb threats, while others have been perpetrated by copycats.
Miller said there are clues that may lead to the primary offender's capture.
"Everything that this individual does, every technological piece that they add in to avoid detection, is going to leave a different kind of fingerprint ... that are going to help identify this person," Miller told "CBS This Morning."
Miller said the main culprit is a man who uses a voice changer to sound on the phone like he is a woman. He also uses voice over internet protocol and phone spoofing to make calls appear to be coming from a number at the Jewish center or school that is the subject of the threat.
CNN called the New York Police Department and was told it has no further comment on the investigation, which is being led by federal agents. The FBI didn't immediately respond to CNN's request for comment.
Law enforcement officials have told CNN they believe many of the threatening calls to Jewish community centers have originated overseas.
Since January, Jewish community centers and schools around the country -- and some in Canada -- have received bomb threats. It started on January 4 with calls made to two Orlando institutions, but the incidents began to spread.
The Anti-Defamation League says there have been 148 threats. The threats have sparked alarm and mass evacuations at community centers and schools. Some parents have pulled their children from JCCs under the continued wave of threats.
There have been no reports that authorities found devices at any of sites.
A former reporter was arrested in St. Louis and accused of making some of the recent bomb threats against Jewish institutions. Juan Thompson, 31, was charged with one count of cyberstalking for allegedly making at least eight threats. He has not entered a plea.