James Siehien, 52, is accused of robbing two of the six banks twice and also robbing a convenience store and a fast-food restaurant, they said.
The robberies all occurred between Oct. 4 and Nov. 5, when police say Siehien was arrested without incident following a holdup.
A criminal complaint said Siehien would pass demand notes to bank tellers and sometimes threaten them with weapons like a machete or an ax.
Authorities said nobody was physically injured in any of the robberies.
The FBI’s Southern Arizona Crime and Gang Task Force worked with Tucson police to make the arrest in the case.
It was unclear Sunday if Siehien had a lawyer yet who could speak on his behalf.
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