The father of New York bombing suspect Ahmad Khan Rahami says the FBI has made "mistake after mistake" in handling the case and is now "punishing" the family for his son's wrongdoing by barring them from travelling to the United States.

Speaking to The Associated Press Saturday, Mohammed Rahami says the FBI did not "do its job properly" by failing to act in 2014 when he contacted investigators with concerns his son could be a terrorist.

He says U.S. authorities recently turned back his wife and son when they tried to travel from Afghanistan to the U.S.

Ahmad Khan Rahami is accused of planting bombs in New York and New Jersey that wounded 31 people last month. The Afghan-born U.S. citizen remains hospitalized with gunshot wounds after a police shootout.