One of several explosive devices discovered in a suspicious package at a train station in the north-eastern US state of New Jersey detonated early Monday as bomb experts were working to defuse it, the FBI said.

The package was discovered late Sunday at the Elizabeth Train Station, the FBI's Newark branch tweeted, adding that no one was injured in the unintentional detonation.

Security forces in the east-coast states of New York and New Jersey have been on edge in the wake of two explosions that occurred on the weekend, the first along the planned route of a US Marines-sponsored charity run in New Jersey on Saturday, and the second in the popular Manhattan neighbourhood of Chelsea later that evening.

No one was injured in the New Jersey blast, while the Chelsea bombing injured 29 people and prompted the discovery of a second device blocks away in Manhattan.

The incidents have prompted New York state officials to tighten security, just as the annual UN General Assembly debates ramp up this week.

US broadcaster ABC News reported that train services were suspended in Elizabeth, New Jersey, as the Federal Bureau of Investigation and a bomb squad were looking into a possible pipe bomb found in garbage at a train station.

The blast on Saturday night in New York City's hip Chelsea neighbourhood destroyed a garbage bin. The site is 3 kilometres from United Nations headquarters on the East River.

New York Mayor Bill de Blasio on Sunday vowed a "bigger than ever" police presence to protect the UN.

The US Homeland Security Department was "actively monitoring and participating in the investigations" of both the New York and New Jersey explosions, Homeland Security Secretary Jeh Johnson said.

He noted that the UN General Assembly debate, which begins Tuesday, was already designated a national special security event, for which thousands of federal personnel led by the Secret Service were deploying to the city.

"Any area in New York City associated with UNGA will therefore be subject to an extraordinarily high level of surveillance and security," Johnson said.

US President Barack Obama was to meet Monday with Chinese Premier Li Keqiang and later Iraqi Prime Minister Haider al-Abadi at the Lotte New York Palace Hotel.

Obama was to visit the US mission outside the United Nations and spend the night in the city, before co-hosting a Tuesday summit on the global refugee crisis.

New York Governor Andrew Cuomo ordered 1,000 additional police officers and National Guard members to patrol New York streets after the Chelsea bombing, which authorities have so far not tied to international terrorism.

The bomb appeared to have been built from a pressure cooker, much like a second, unexploded device found minutes later, a few blocks from the blast site.

"We will find whoever did this or whatever group did this, and they will be brought to justice, period," Cuomo said.

Broadcaster CNN reported that a investigators have spotted a man pulling a piece of wheeled luggage on surveillance videos from the explosion site.

A few minutes later, the same man was captured by another security camera leaving the bag at the site where the unexploded device was found.

The video then shows two men open the suitcase, remove a plastic sack that apparently contained the second device, and leave with the suitcase.

The New York City blast occurred hours after a bomb hidden in a garbage container exploded Saturday in the neighbouring state of New Jersey along the planned route of a charity run sponsored by the US Marines, causing no injuries.

Authorities have not revealed direct links between the New Jersey and New York cases.

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