The father, Mohammad Rahami, said in an interview published on ABC's website on Wednesday that his wife, Najiba, and another of his sons, Qassim, were in Dubai when they were pulled from a flight and questioned for 16 hours by authorities there.
Authorities then sent them to Kabul, he said.
"Why send my son back to Afghanistan? He is a US citizen. You have any questions? Bring him home, [don't] send him to a different country," Mohammad Rahami said of Qassim.
New York bomb suspect's family clashed with New Jersey city over restaurant
Reuters could not immediately confirm that the two were being held.
Ahmad Rahami, a 28-year-old naturalized US citizen, emigrated from Afghanistan with his family at the age of 7. They settled in Elizabeth, New Jersey, and opened a fried chicken restaurant.
Rahami faces federal charges in the bombing this month that injured 31 people in Manhattan's Chelsea neighborhood, and in connection with explosives found at locations in New Jersey. No one was killed in the blasts.
New York bomb suspect charged with attempted murder
Rahami has been held in a Newark, New Jersey, hospital since his arrest last week with wounds after a shootout with police.
Investigators have probed Rahami's history of travel to Afghanistan and Pakistan. He was motivated by militant views, prosecutors say, citing a journal he carried when he was captured in which he begged for martyrdom and expressed outrage at what he called the US slaughter of Muslim fighters.
The American Civil Liberties Union said on Monday it will temporarily provide legal counsel to Rahami, as concern grew over his lack of access to a lawyer. Authorities say Rahami is not physically able to appear in court, and he has not.
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