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8 year oldMr Cuomo said significant damage had been caused and "we were lucky there were no fatalities". Saturday night's blast in Manhattan injured 29 people.
Some 1,000 extra security personnel are being deployed to NY transport hubs.
Mr Cuomo said: "Whoever placed these bombs - we will find them and they will be brought to justice."
A second device - 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.
Addressing reporters on Sunday near the site of the explosion, 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."
All 29 injury victims had now been released from hospital, he said.
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.
The Chelsea explosion occurred at about 21:00 (01:00 GMT on Sunday), outside a residence for blind people on West 23rd St.
The second device has been described as a pressure cooker attached to wiring and a mobile phone - and this mode of attack was last seen in the US during the Boston Marathon bombings of 2013.
A pressure cooker device also featured in a failed jihadist plot to attack New York's Times Square in 2010. Extreme right-wing cells have also made them and the instructions are freely passed around on the internet.
The US has a dedicated laboratory where forensic scientists analyse the remains of every significant explosive device the security services recover.
Tiny fragments of a detonated device can be enough to pinpoint how it was made - and potentially who made it. Two years ago the US scientists had a major victory when their painstaking work uncovered evidence that proved that a London taxi driver had made bombs in Iraq that killed a soldier.
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.
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.
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