In every case, the threatening letters contained a white powder that is apparently harmless.
Among the banks receiving the letters was the Chase Bank on Kennedy Blvd. in Lakewood, New Jersey.
It's one of six Chase locations in New Jersey that received a letter.
Additional tests were being run on the letters Tuesday as officials zeroed in on possible suspects near Amarillo, Texas, where the letters were postmarked.
"Most of these letters contain a powder substance with a threatening communication," the FBI said in a statement.
"Even sending a hoax letter is a serious crime," the FBI said.
All of the letters appear to be from the same source and began showing up at the banks on Monday, according to the official who spoke on condition of anonymity because he was not authorized to discuss the matter publicly.
A second law enforcement official, also speaking anonymously under the same conditions, said authorities were looking into whether the letters were sent in anger due to the cratering economy. Authorities would not release the text of the letters, but Gary Johnson, a spokesman at the FBI field office in Oklahoma City, said the threat was "based on past actions of the bank" and that the letters implied that the opener was going to die.
No injuries were reported after any of the letters were opened. Mary Jane Rogers, a spokeswoman for JP Morgan Chase & Co., said some employees, including a pregnant woman, were examined as a precaution.
Additional reporting by the Associated Press