The president spoke at an interfaith vigil during his visit, the fourth time he has traveled to a city after a mass shooting.
"We gather here in memory of 20 beautiful children and six remarkable adults," Mr. Obama said. "They lost their lives in a school that could've been any school, in a quiet town full of good and decent people that could've been in any town in America."
"You're not alone in your grief," the president said. "All across this land of ours, we have wept with you."
Mr. Obama did not specifically address gun control. But he said "We can't tolerate this anymore.These tragedies must end and to end them we must change."
Earlier in the day, the president met with the victims' families and met with first responders.
Just a day prior, state police released the names of the 20 children and six adults who were killed in the shooting rampage at Sandy Hook Elementary School. The kids, eight boys and 12 girls, were mostly 6 or 7 years old. All of the adult victims, which included the school principal and the psychologist, were women.
Earlier Sunday morning, a credible threat forced the evacuation of St. Rose of Lima Catholic Church. The threat was deemed over and armed state troopers exited the church, but it still rattled many churchgoers, who were already on edge and shattered from the shooting.
See the complete list of victims' names released by Connecticut police
Police said the suspected gunman, identified by authorities as 20-year-old Adam Lanza, forced his way into the school Friday morning armed with hundreds of round and fired off shots, as teachers locked doors and children huddled in corners or hid in closets. According to ABC News, Lanza shot and shattered windows at the front of the school to get inside.
Based on the Sandy Hook school directory, all the kids killed were in the first grade. Police said the shooting happened in one section of the school in two rooms.
In one classroom, 15 students were killed. In the other class, five students died along with their teacher, Victoria Soto. Also, nine of the deceased students have siblings in the school.
Speaking on ABC's "This Week," Connecticut Gov. Dannel Malloy said Lanza shot himself as police entered the building.
"We surmise that it was during the second classroom episode that he heard responders coming and apparently at that, decided to take his own life," Malloy said.
Malloy offered no possible motive for the shooting and a law enforcement official has said police have found no letters or diaries left behind that could shed light on it.
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During a Saturday press conference, however, investigators said they've discovered "very good evidence" at both the school and Lanza's mother's home. He said that evidence is beginning to paint a complete picture of the motive. He refused to elaborate on exactly what was found at the crime scenes.
Investigators said Lanza had also shot and killed his mother at her home before he drove to the school to continue the shooting spree then took his own life.
ABC News reports Lanza's mother and father were both registered gun owners.
During a Sunday afternoon news conference, Connecticut State Police Lt. Paul Vance confirmed details of four weapons found at the shooting site. A Bushmaster AR-15 assault-style rifle with a high-capacity magazine was the primary weapon used to murder those at the school. Vance said there was also a 10 mm Glock and a 9 mm Sig Sauer. The fourth gun was a shotgun recovered from Lanza's vehicle.
Federal authorities told ABC News that it appears likely that at least some of the guns used in the shooting belonged to Nancy Lanza and were legally registered, but some of the gun traces have not yet been completed.
Vance said Lanza used a handgun to commit suicide. Vance also said there were many magazines found at the scene, with hundreds of bullets in them. He told ABC News earlier that "without a question," he would have killed more people had first responders not arrived.
Adam Lanza was a student at Sandy Hook and his mother used to work there as a teacher's aide, according to Lanza's aunt, Marsha Lanza. However, the school district has told ABC News that they can find no records that Nancy worked at Sandy Hook. Also, several current employees at the school said they have no recollection of her having worked there in recent years.
Questions still unanswered include: Why did his mother, a well-to-do suburban divorcee, keep a cache of high-power weapons in the house? What experience did Lanza have with those guns? And, above all, what set him on a path to shoot and kill 20 children, along with the adults who tried to stop him?
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All the victims at the school were shot with a rifle, at least some of them up close, and all were apparently shot more than once, Chief Medical Examiner Dr. H. Wayne Carver said. There were as many as 11 shots on the bodies he examined.
This unthinkable tragedy has plunged Newtown into mourning and added the New England community of 27,000 people to the grim map of towns where mass shootings in recent years have periodically reignited the national debate over gun control but led to little change.
Watch Pres. Obama's national address about the Sandy Hook shooting
Saturday night, overflow crowds packed St. Rose of Lima Roman Catholic Church. The Rev. Richard Scinto, a deacon, gave a homily.
"In the past 48 hours I've said the phrase 'I don't know' about 1,000 times," he said. "That not knowing has got to be the worst part of this whole thing."
In the Vatican, Pope Benedict XVI told pilgrims and tourists Sunday that he is praying for the families of the victims.
"I assure the families of the victims, especially those who lost a child, of my closeness in prayer," the pope said. "May the God of consolation touch their hearts and ease their pain."
See photos from the Sandy Hook school shooting in Connecticut
Peter Lanza, Adam Lanza's father, addressed the shooting in a statement on Saturday.
"Our hearts go out to the families and friends who lost loved ones and to all those who were injured," he said. "Our family is grieving along with all those who have been affected by this enormous tragedy. No words can truly express how heartbroken we are. We are in a state of disbelief and trying to find whatever answers we can. We too are asking why. We have cooperated fully with law enforcement and will continue to do so. Like so many of you, we are saddened, but struggling to make sense of what has transpired."
Mr. Obama and Senate Democrats haven't pushed for new gun controls since rising to power in the 2008 national elections. Outspoken advocates for stricter laws, including Sen. Dianne Feinstein, say that's because of the powerful sway of the National Rifle Association.
But advocates also say the latest shooting is a tipping point that could change the dynamic of the debate dramatically. Feinstein, D-Calif., said she will propose legislation next year that would ban big clips, drums and strips of more than 10 bullets.
To make a contribution to the Newtown Memorial Fund please visit: http://www.newtownmemorialfund.org/
ABC News and Associated Press contributed to this report.
