Nafis' father Quazi Ahsanullah called on the government to help bring his son back home.
The arrest made headlines in Dhaka newspapers and caused Bangladeshis to worry it would hurt their country's image as a moderate Muslim nation.
"I don't know if this kid is actually involved in the plot, but the incident does not help our image abroad," said Harun Rashid, a resident in Dhaka.
Prosecutors said Nafis traveled to the United States on a student visa in January to carry out an attack.
A few hours before he was arrested, Nafis calmly spoke via Skype with his parents back home and updated them on his studies, his family told the Associated Press.
Nafis attended Southeast Missouri State University during the spring semester, which ended in May, in pursuit of a bachelor's degree in cybersecurity, university spokeswoman Ann Hayes said.
A classmate there said he often remarked that true Muslims don't believe in violence.
"I can't imagine being more shocked about somebody doing something like this," said Jim Dow, 54, an Army veteran who rode home from class with Nafis twice a week. "I didn't just meet this kid a couple of times. We talked quite a bit. . . . And this doesn't seem to be in character."
Federal investigators, often accused by defense attorneys of entrapping and leading would-be terrorists along, said Nafis made the first move over the summer, reaching out for accomplices and eventually contacting a government informant, who then went to federal authorities.
Investigators would not say exactly how he initially contacted the informant.
They said he also selected his target, drove the van loaded with dummy explosives up to the door of the bank, and tried to set off the bomb from a hotel room using a cellphone he thought had been rigged as a detonator.
During the investigation, he and the informant corresponded via Facebook and other social media, talked on the phone, and met in hotel rooms, according to a law enforcement official who was not authorized to speak publicly and spoke on condition of anonymity.
Nafis spoke of his admiration for Osama bin Laden, talked of writing an article about his plot for an al-Qaeda-affiliated magazine, and said he would be willing to be a martyr but preferred to go home to his family after carrying out the attack, authorities said.
Investigators said in court papers that he came to the United States bent on jihad and worked out the specifics of a plot when he arrived. While Nafis believed he had the blessing of al-Qaeda and was acting on behalf of the terrorist group, he has no known ties, according to federal officials.