The man made a video before the attack, saying he wanted to "kill as many of them as I possibly can," said Jennifer Runyan, head of the FBI in Detroit.
Federal prosecutors charged Omar Alkattoul, 18, with one count of transmitting a threat in interstate and foreign commerce.
The FBI said Friday that it's identified the "source of the threat" made against "an unspecified New Jersey area synagogue."
The pair "remain in custody for questioning," police said.
President Biden and the U.S. Federal Bureau of Investigation are now calling Saturday morning's events at Beth Israel Synagogue in Colleyville, Texas, an "act of terror" in which the Jewish community was directly targeted.
An armed suspect claiming to have bombs in unknown locations took a rabbi and three others hostage at the Congregation Beth Israel in Colleyville.
