City officials called on the public to help them track down who's responsible.
Investigators are also combing through surveillance video for clues, but so far they haven't found anything pointing to a suspect, a senior law enforcement official said. Some of the video is not helpful because the cameras are either too far away or the footage is too grainy to tell what's on it, the official said. Investigators will be canvasing for additional video Sunday.
Authorities have cordoned off the street where the explosion occurred, in the Chelsea neighborhood south of Midtown in western Manhattan. A small crowd watched from behind police tape Sunday as investigators gathered at the blast site. Some onlookers said residents who live on the block still hadn't been allowed to return to their homes.
Investigators are still searching the scene for evidence, officials said.
"The evidence we've collected is being taken to our lab at Quantico for review, and we are following every available lead," FBI Assistant Director in Charge William Sweeney Jr. said Sunday.
Meanwhile, New Yorkers will see an increased police presence around the city, de Blasio said.
Stepped-up security across the city is common as world leaders arrive for the United Nations General Assembly meeting, which is underway. But now it will be even more intense, de Blasio said.

"You should know you will see a very substantial NYPD presence this week -- bigger than ever," he said.
And New York Gov. Andrew Cuomo said 1,000 additional New York State Police officers and National Guard troops will be deployed to patrol bus terminals, airports and subway stations.
The increased policing, Cuomo said, is "just to err on the side of caution."
"I want New Yorkers to be confident when they go back to work on Monday that New York is up and running and we're doing everything that we need to do," he said.
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Suspicious device found nearby
Police officers and federal agents searched the streets with flashlights, robots and dogs early Sunday to ensure there were no other devices in the area.
Multiple local and federal law enforcement officials described the pressure cooker found at 27th Street. None of them would say what was inside the cooker, which has since been removed from the scene.
A device at a second location in Chelsea appears to be a pressure cooker, according to multiple local and federal law enforcement officials.
A piece of paper with writing on it was found nearby, the officials said.
Search attention also focused on another object in the area, but it turned out to be trash.
De Blasio said investigators believe there is no connection to an earlier incident in New Jersey,where an explosion went off in a garbage can on the route of a Marine Corps charity run Saturday.
The New York explosion caused "significant property damage," Cuomo said.
"We really were lucky that there were no fatalities," he said.
By Sunday morning, all 29 injured victims had been released from hospitals, the governor said.
Is it terrorism?
New York's governor didn't mince words Sunday when he talked about the explosion.
"A bomb exploding in New York is obviously an act of terrorism," Cuomo said, vowing that authorities would catch whoever is responsible.
"A bomb going off is generically a terrorist activity. That's how we'll consider it. And that's how we will prosecute it," he said.
But law enforcement officials and the city's mayor cautioned that without a known motive, it's too soon to call the bombing a terror attack.
CNN law enforcement analyst Tom Fuentes said the information authorities have revealed so far about the blast leads him to a troubling conclusion.
"It tells me that it was a rather large explosive device that someone built and someone detonated and caused the injury of dozens of people. ... It shows me it's a deliberate act and indicates an act of terrorism," he said. "Whether it's domestic terrorism or international, we don't know, but it certainly would have an appearance that somebody made an attempt to kill people, on purpose."
But CNN national security analyst Juliette Kayyem said it's too soon to label the blast a terror attack without knowing the motivations behind the explosion. Terrorism, she said, generally has political or religious motives behind it.
"I think it's premature to call it terrorism until we know -- unless you want to define terrorism as any violent act in an urban area -- but given that there's no proof of motivation, you wouldn't be able to bring a terrorism case, so to speak, today," she said. "You certainly would be able to bring other types of cases if you found the culprit."
'I could feel it in my chest'
The explosion rocked Chelsea, a New York neighborhood that's packed with restaurants, subway stations, shops, businesses and art galleries.
Nearby resident Sam Smith, 50, said he was closing the shades of his apartment when the blast hit.
"All I saw was a big light, and then I heard the explosion," he told CNN as he watched investigators and waited for word about whether he could return home Sunday morning. "I could feel it in my chest. It took me an hour and a half before I could hear again."
Danilo Gabrielli, 50, was watching TV at his 23rd Street apartment about a block away from the explosion site when he heard the blast. He rushed to see what had happened and found a chaotic scene.
"We smelled something, like an intense sulfur smell, and saw smoke coming out of this building. I saw pieces of metal -- not large, but not small either. A few friends of mine saw glass there."
Gabrielli said "the entire neighborhood is real scared."
"It's a real quiet neighborhood -- not like the center of the city or the Wall Street area. It's tiny bars, where you go to grab a drink, grab a bite to eat, watch a film. We were worried."
Surveillance video shows windows shattered with terrified people running on the streets and ducking. The video, which shows angles from inside and outside Orangetheory Fitness in Chelsea, shows a screen laying outside on the street after the explosion and what appears to be papers flying in the air.
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Surveillance video shows the impact from the explosion.
Some social media users said the sound of the explosion was heard as far away as Hoboken, New Jersey, across the Hudson River.