The backpack in Elizabeth was discovered on Sunday evening by two men scavenging trash who reported the package to police after seeing "wires and a pipe", Bollwage said.
Federal Bureau of Investigation agents are questioning five suspects over the explosion that injured 29 people in a crowded Manhattan neighbourhood.
Two homeless men found a backpack in the trash, thinking there was something of value in it.
Elizabeth Mayor Christian Bollwage said the device exploded shortly after 12:30 a.m. Monday.
No injuries were reported in the explosion, which went off when a bomb robot was examining it, the reports said.
No suspects were immediately identified in the NY and New Jersey attacks or the latest incident in Elizabeth.
"There is considered to be a heightened threat of terrorist attacks globally against United Kingdom interests and British nationals, from groups or individuals motivated by the conflict in Iraq and Syria".
Police officers stand near the area where an explosive device left at a train station was detonated by the authorities in Elizabeth, New Jersey, U.S., September 19, 2016. One of the explosive devices had the suspect's fingerprint on it. I know there are other devices.
The FBI reviewed its databases and found no credible connection to terrorism or threat to the USA from the son, the official said. Their identities have yet to be revealed, and nobody has been charged with a crime at this time.
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Up to five devices were found in the bag and when the robot cut a wire on one of them to try and disable it, it exploded.
"The Department of Homeland Security is actively monitoring and participating in the investigations of the explosions in NY and New Jersey yesterday", Secretary Jeh Johnson said.
Authorities questioned several people early Monday after a auto stop in New York City as they worked to determine whether there was a connection between several explosive devices found in two states in two days.
Ryan McCann, of Elizabeth, said that he often ate at the restaurant and recently began seeingRahami working there more.
Also on Saturday, a man who authorities say referred to Allah wounded nine people in a stabbing rampage at a Minnesota mall before being shot to death by an off-duty police officer.
The shootout came after a weekend of fear and dread in NY and New Jersey.
Mayor Chris Bollwage said the Union County Bomb Squad determined it could be a bomb.
This follows the explosion of a pipe bomb on Saturday in the New Jersey town of Seaside Park, some 80 miles south of New York City. A second device that did not explode was also found in the area.
"In many of these cases we don't know until two, three or four days later whether or not there is a terrorist link", warned New York Congressman Peter King in a CBS television interview.
