The father of a man arrested over the weekend bombings in New York and New Jersey called the FBI in 2014 to say his son was a terrorist but later retracted the claim, a law enforcement official has said.

The father contacted the FBI after Ahmad Khan Rahami was charged with stabbing his brother, according to the official, who was not named.

The official said the FBI looked into the matter, but that the father, Mohammad Rahami, retracted his comment and said he meant his son was spending time with the wrong crowd.

The FBI reviewed its databases and found no credible connection to terrorism or threat to the US from the son, the official said.

The information emerged as Rahami, 28, was being held on $5.2 million bail, charged with five counts of attempted murder of police officers following the shoot-out that led to his capture.

Federal prosecutors said they were considering charges over the bombings that wounded 29 people.

Rahami, a US citizen born in Afghanistan, remained in hospital after surgery for a gunshot wound to his leg. He was arrested in Linden, New Jersey, after he was found sleeping in the doorway of a bar.

His father told reporters outside the family's fried chicken restaurant in Elizabeth, New Jersey, that he called the FBI two years ago. But asked whether he thought his son was a terrorist, the father said: "No. And the FBI, they know that."

Ahmad Khan Rahami was arrested in 2014 on charges of stabbing a person in the leg and possession of a firearm. A grand jury declined to indict him, despite a warning from the arresting officer that Rahami was probably "a danger to himself or others".

William Sweeney, the FBI's assistant director in New York, said the FBI had received a report of a domestic incident involving Rahami some time ago, but the allegations had been recanted, and "there's nothing to indicate that currently he was on our radar".

The bombing investigation began when a pipe bomb blew up on Saturday morning in Seaside Park, New Jersey, before a charity race to benefit Marines. No one was injured.

Then a shrapnel-packed pressure-cooker bomb exploded on Saturday night in New York's Chelsea section, wounding 29 people, none seriously. An unexploded pressure-cooker bomb was found blocks away.

Late on Sunday night, five explosive devices were found in a rubbish bin at an Elizabeth train station. Investigators have not publicly tied Rahami to those devices.

Rahami provided investigators with a wealth of clues that led to his arrest just 50 hours after the first explosion, according to three law enforcement officials.

His fingerprints and DNA were found at the scene of the Manhattan bombing, they said. His face was clearly captured by surveillance cameras near the spot of the blast.

Electronic toll records show a car to which he had access was driven from New Jersey to Manhattan and back to New Jersey on the day of the bombing, according to the officials.

Those and other clues prompted officials to release his name and photo on Monday morning.

"A lot of technology was involved in this, but a lot of good, old-fashioned police work, too," New York Police Commissioner James O'Neill said.

Officials said they have no other suspects at large but added they are still investigating.

Rahami was not on any terror or no-fly watch lists, though he had been interviewed for immigration purposes while travelling between the US and Afghanistan, one of the law enforcement officials said.

Rahami and his family live above their restaurant, First American Fried Chicken, and the family has clashed with the city over closing times and noise complaints.