BOSTON — Federal agents zeroed in Tuesday on how the Boston Marathon bombing was carried out — with kitchen pressure cookers packed with explosives, nails and other lethal shrapnel — but said they still didn’t know who did it and why.

An intelligence bulletin issued to law enforcement and released late Tuesday included a picture of a mangled pressure cooker and a torn black bag the FBI said were part of a bomb.

The FBI and other law enforcement agencies repeatedly pleaded for members of the public to come forward with photos, videos or anything suspicious they might have seen or heard.

“The range of suspects and motives remains wide open,” Richard DesLauriers, FBI agent in charge in Boston, said at a news conference. He vowed to “go to the ends of the Earth to identify the subject or subjects who are responsible for this despicable crime.”

President Barack Obama branded the attack an act of terrorism but said officials don’t know “whether it was planned and executed by a terrorist organization, foreign or domestic, or was the act of a malevolent individual.”

Scores of victims remained in hospitals, many with grievous injuries, a day after the twin explosions near the marathon’s finish line killed three people, wounded more than 170 and reawakened fears of terrorism. A 9-year-old girl and 10-year-old boy were among 17 victims listed in critical condition.

Officials found that the bombs consisted of explosives put in ordinary 1.6-gallon pressure cookers, one with shards of metal and ball bearings, the other with nails, according to a person close to the investigation who spoke on condition of anonymity because the probe was still going on. The bombs were stuffed into black duffel bags and left on the ground, the person said.

DesLauriers confirmed that investigators had found pieces of black nylon from a bag or backpack and fragments of BBs and nails, possibly contained in a pressure cooker. He said the items were sent to the FBI laboratory at Quantico, Va., for analysis.

The FBI said it is looking at what Boston television station WHDH said are photos sent by a viewer that show the scene right before and after the bombs went off. The photo shows something next to a mailbox that appears to be a bag, but it’s unclear what the significance is.

“We’re taking a look at hundreds of photos, and that’s one of them,” FBI spokesman Jason Pack said.

Investigators said they haven’t determined what was used to set off the explosives.

Pressure cooker explosives have been used in international terrorism and have been recommended for lone-wolf operatives by al-Qaida’s branch in Yemen.

But information on how to make the bombs is readily found online, and U.S. officials said Americans should not rush to judgment in linking the attack to overseas terrorists.

DesLauriers said there had been no claim of responsibility for the attack.

He urged people to come forward with anything suspicious, such as hearing someone express an interest in explosives or a desire to attack the marathon, seeing someone carrying a dark heavy bag at the race or hearing mysterious explosions recently.

“Someone knows who did this,” the FBI agent said.

The bombs exploded 10 or more seconds apart, tearing off victims’ limbs and spattering streets with blood, instantly turning the festive race into a hellish scene of confusion, horror and heroics.

The blasts killed 8-year-old Martin Richard, of Boston, 29-year-old Krystle Campbell, of Medford, and a third victim, identified only as a graduate student at Boston University.

The Chinese Consulate in New York said the third person was a Chinese national. An official at the consulate’s press section, who was not authorized to give his name, said that one Chinese student was injured and another died in the blast.

The official said a work group from the consulate was in Boston to investigate the situation and assist relatives of the victims.

The official Chinese news agency Xinhua reported that relatives have requested that the deceased not be identified.

Doctors who treated the wounded corroborated reports that the bombs were packed with shrapnel.

“We’ve removed BBs, and we’ve removed nails from kids. One of the sickest things for me was just to see nails sticking out of a little girl’s body,” said Dr. David Mooney, director of the trauma center at Boston Children’s Hospital.

At Massachusetts General Hospital, four amputations performed there were above the knee, with no hope of saving more of the legs, said Dr. George Velmahos, chief of trauma surgery.

“It wasn’t a hard decision to make,” he said. “We just completed the ugly job that the bomb did.”

Obama plans to visit Boston on Thursday to attend an interfaith service in honor of the victims. He has traveled four times to cities reeling from mass violence, most recently in December after the school shootings in Newtown, Conn.

In the wake of the attack, security was stepped up around the White House and across the country. Police massed at federal buildings and transit centers in the nation’s capital, critical response teams deployed in New York City and security officers with bomb-sniffing dogs spread through Chicago’s Union Station.

Homeland Security Secretary Janet Napolitano said that the stepped-up security was a precaution and that there was no evidence the bombings were part of a wider plot.

Pressure cooker explosives have been used in Afghanistan, India, Nepal and Pakistan, according to a July 2010 intelligence report by the FBI and the Department of Homeland Security. One of the three devices used in the May 2010 Times Square attempted bombing was a pressure cooker, the report said.

“Placed carefully, such devices provide little or no indication of an impending attack,” the report said.

The Pakistani Taliban, which claimed responsibility for the 2010 attempt in Times Square, has denied any part in the Boston Marathon attack.

Al-Qaida’s branch in Yemen gave a detailed description of how to make a bomb using a pressure cooker in a 2010 issue of Inspire, its English-language online publication aimed at would-be terrorists acting alone.

“This is probably one of the most photographed areas in the country yesterday,” said Boston police Commissioner Edward Davis. He said two security sweeps of the marathon route had been conducted before the bombing.

Boston police and firefighter unions announced a $50,000 reward for information leading to arrests.