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8 year oldTwenty-nine people were injured when a bomb went off in the Chelsea neighbourhood of Manhattan on Saturday.
Mr Rahami was already charged by the state of New Jersey with the attempted murder of police, during his arrest.
The new federal charges include use of a weapon of mass destruction, bombing, destruction of property and use of a destructive device.
Investigators say Mr Rahami, who is 28, planted two bombs in Chelsea but one failed to detonate.
Another bomb exploded in a New Jersey seaside town earlier on the same day but no-one was hurt.
He is also accused of leaving explosives in a discarded rucksack in a rubbish bin in Elizabeth, New Jersey.
The series of bombings over the weekend have sparked a heated debate about national security between the two presidential candidates, days before their first televised debate.
Republican Donald Trump has seized on the fact Mr Rahami was born in Afghanistan to bolster his tough stance on immigration admissions.
But his Democratic rival, Hillary Clinton, has accused Mr Trump of enabling the terrorists by playing into their hands.
Mr Rahami is still in hospital, recovering from injuries sustained during the shootout that led to his arrest.
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