The bomb detonated on Saturday in New York, and another device found nearby, were both shrapnel-filled pressure cookers - similar to the bombs used at the 2013 Boston Marathon, reports say.
Citing top law enforcement officials, the New York Times said the two devices used flip phones and Christmas lights designed to trigger the explosive.
The blast, in the Chelsea area of Manhattan, injured 29 people.
Officials call it a terror act, but no motive or suspect has been identified.
The second device was found four blocks from the site of the explosion and was removed safely.
New York governor Andrew Cuomo said it appeared to be "similar in design" to the exploded device.
Both were different from a pipe bomb that detonated earlier on Saturday on the route of a charity race in New Jersey, Mr Cuomo added. That explosion caused no injuries.
The unexploded second device was destroyed by police in a controlled explosion late on Sunday.
No group has said it carried out the attack.
New York Mayor Mayor Bill de Blasio said: "Was it a political motivation? A personal motivation? We do not know."
"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."
Mr Cuomo said: "Whoever placed these bombs - we will find them and they will be brought to justice."
Some 1,000 extra security personnel are being deployed to New York's transport hubs, police said.
Windows blown out
The Chelsea explosion occurred at about 21:00 (01:00 GMT on Sunday) 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.
In the Boston Marathon bombing in April 2013, two pressure-cooker bombs packed with shrapnel exploded near the finish line, killing three spectators and injuring about 280.
A police officer was killed during the operation to catch suspects Dzhokhar and Tamerlan Tsarnaev, two brothers believed to have converted to radical Islamists. Tamerlan Tsarnaev died in a shoot-out.
CCTV captures moment of blast
No quick answers - mayor
How the election candidates reacted - BBC's Anthony Zurcher
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.