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8 year old"Was it a political motivation? A personal motivation? We do not know," said Mayor Bill de Blasio.
Saturday night's blast in Manhattan injured 29 people. They have all now been released from hospital.
NY Governor Andrew Cuomo said: "Whoever placed these bombs - we will find them and they will be brought to justice."
A second device - reportedly a pressure cooker attached to wiring and a mobile phone - had been found four blocks from the site of the explosion in the Chelsea district and was removed safely.
Police said the device would be destroyed in a controlled explosion later on Sunday.
Mr de Blasio told reporters: "We know there was a bombing. We know it's a very serious incident. But we have a lot more work to do to be able to say what kind of motivation was behind this.
"All possible theories of what's happened here and how it connects will be looked at but we have no specific evidence at this point in time."
The mayor vowed: "We will keep the public informed every step of the way."
Speaking earlier near the site of the blast, Mr Cuomo said significant damage had been caused and "we were lucky there were no fatalities".
Some 1,000 extra security personnel are being deployed to New York's transport hubs.
Mr Cuomo said: "A bomb exploding in New York is obviously an act of terrorism."
But he said that, as yet, no international organisation such as so-called Islamic State had claimed they were behind it.
Mr Cuomo said: "We will not allow these type of people and these type of threats to disrupt our life in New York. This is freedom. This is democracy, and we are not going to allow them to take that from us.
"They want to instil terror. They want to make you worry about going into New York. We're not going to let them instil fear."
Mr Cuomo said that the attack was one of the "nightmare scenarios" a governor must face, but he added: "We have no reason to believe at this time that there is any further immediate threat."
He said the two devices in New York appeared similar in design, but different from the pipe bomb that detonated earlier on Saturday on the route of a charity race in New Jersey. That explosion caused no injuries.
Governor Andrew Cuomo called it a politician's "nightmare scenario" - a late-night phone call with news of a crisis. The weekend's attacks in New York, New Jersey and Minnesota have put national security squarely back in the centre of the US presidential election.
A similar scenario unfolded in June following the Orlando nightclub shootings. That was an opportunity for Donald Trump - the "change" candidate who touts his hard line on security issues - to make his case... and he blew it. Mrs Clinton's lead grew as Americans soured on Mr Trump's bellicose response.
This time Mr Trump has been more measured, offering only condolences on Twitter. He did call the New York incident a "bombing" before official confirmation and said the US needed to "get tough", but that was hardly comparable to his jarring comments on Orlando.
Meanwhile, Mrs Clinton cautioned against premature conclusions - perhaps hoping her opponent would again overreact.
With the race tight once again and the first TV debate just over a week away, both candidates are under intense pressure to display their leadership qualities. Saturday's "nightmare scenario" was another test - and it probably won't be the last.
The Chelsea explosion occurred at about 21:00 (01:00 GMT on Sunday), outside a residence for blind people on West 23rd St.
The force of the blast blew out windows and could be heard several blocks away.
Some reports said the bomb went off in a black metal construction toolbox, others that it was in a rubbish bin.
Police refused to give many more details on Sunday, although New York Police Commissioner James O Neill said that "components indicative of an IED" (improvised explosive device) had been found.
Chelsea is among the most fashionable districts of Manhattan and its bars and restaurants are usually crowded at the weekend.
On Tuesday President Obama and other world leaders are due to attend the UN General Assembly in New York.
Mr de Blasio said there would be a "bigger than ever" police presence in New York in the coming week.
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