Barack Obama said he would use the powers of his office to prevent a repeat of the tragedy.
He told residents that the nation shared their grief.
Twenty children and six women died in the assault on Sandy Hook school by a lone man who then took his own life.
The first funerals for victims will be held on Monday.
The gunman has been identified by police as Adam Lanza, 20.
He shot dead his mother before driving to the school in her car.
Officials say he was armed with hundreds of rounds of ammunition, and used a semi-automatic rifle as his main weapon. He was also carrying two handguns, and a shotgun was recovered from a car.
“I come to offer the love and prayers of a nation,” Barack Obama said, speaking after religious leaders and the state governor.
“You are not alone in your grief. All across this land of ours we have wept with you.”
Barack Obama repeated a call for action against gun crime, saying that in coming weeks he would use “whatever powers” his office held “in an effort aimed at preventing more tragedies like this”.
“We can’t tolerate this anymore,” he said.
“These tragedies must end and to end them we must change.”
The complex causes of gun crime “can’t be an excuse for inaction”, he said.
Barack Obama was also meeting victims’ families and emergency service workers.
All 20 children who died in the shootings – eight boys and 12 girls – were aged between six and seven, according to an official list of the dead. The school’s head teacher, Dawn Hochsprung, was among those killed.
All victims were shot several times, some of them at close range.
Police say the process of releasing the victims’ bodies to their families is under way.
Barack Obama made an appeal for “meaningful action” against gun crime in the US shortly after the attack on Friday.
Sunday saw two senior US Democrats call for stricter gun control.
Connecticut Governor Dannel P. Malloy said his state had an existing ban on assault weapons, but the lack of a similar law at federal level made it difficult to keep them out of the state.
“These are assault weapons. You don’t hunt deer with these things,” he told CNN.
“One can only hope that we’ll find a way to limit these weapons that really only have one purpose.”
Governor Dannel Malloy had to break the news to most of the victim’s families on Friday.
“You can never be prepared for that – to tell 18 to 20 families that their loved one would not be returning to them that day or in the future,” he said.
Senator Dianne Feinstein, who represents California in the upper house of Congress and is a long-term supporter of stricter gun control, told US TV network NBC: “I’m going to introduce in the Senate, and the same bill will be introduced in the House [of Representatives], a bill to ban assault weapons.”
Asked if President Barack Obama would support her measure, she said: “I believe he will.”
New York Mayor Michael Bloomberg, another strong gun control advocate, has urged President Barack Obama to act.
“We have heard all the rhetoric before,” he said.
“What we have not seen is leadership – not from the White House and not from Congress. That must end today.”
A nationwide ban on certain semi-automatic rifles in the US expired in 2004.
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