President Barack Obama has vowed to use all his power to make sure that shooting tragedies like the one that left 20 young children and six adults dead are not repeated.
He told a vigil in Newton, Connecticut that such killings have to end and there must be change for this to happen.
Lawmakers in the United States are promising to discuss gun control and funding for mental health care after the tragic shooting of 20 children at at Sandy Hook School and six adults on Friday.
Senator Dianne Feinstein of California said she would introduce a bill banning assault weapons as soon as Congress convened.
A nationwide ban on certain semi-automatic rifles in the United States expired in 2004.
Senator Feinstein told NBC TV on Sunday:
"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 Obama would support her measure, she said: "I believe he will."
New York Mayor Michael Bloomberg has urged President 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."
In a national address on Friday, President Barack Obama urged "meaningful action".
Connecticut Governor Dannel Malloy said there will be a time for that discussion soon, but many people are still struggling to come to terms with the massacre.
"There's precious little anyone can say to the families that will lessen the horror and the sense of loss they feel," he said.
"We could say we feel their pain. But the truth is, we can't.
"When tragedies like this take place people often look for answers, an explanation of how this
could have happened. But the sad truth is, there are no answers. No good ones anyway."
Governor Malloy had to break the news to most of the 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.
Friday's toll was the highest since the killings at Virginia Tech in 2007, which left 32 people dead and many wounded.
The ABC reports a gunman killed 12 people in a movie theatre in Colorado in August, 2012. Two weeks later six people were killed at a Sikh temple in Wisconsin.
Two students shot dead 13 people at the Columbine High School in Littleton, Colorado in 1999.
In the latest incident: Adam Lanza, 20, reportedly first killed his mother in their home before going to Sandy Hook School in Newtown on Friday morning to kill the children, their teachers and then himself.
Although he was remembered as shy and awkward, the BBC reports Lanza did not apparently give any warning sign that he was to become a mass murderer.
His mother legally owned a Sig Sauer and a Glock, and a Bushmaster .223 M4 carbine.
Governor Malloy said Connecticut has 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."
The BBC reports other countries have responded by tightening their gun laws following public outcries in the wake of mass shootings.
Access to firearms were restricted in Britain following the Hungerford massacre in 1987 and handguns were effectively banned in the aftermath of a school shooting in Dunblane in 1996.
Australia introduced sweeping new laws after 35 people in Port Arthur, Tasmania, were shot dead in 1996.
Finland - which has some of Europe's most relaxed firearms legislation and highest rates of gun ownership - placed extra restrictions on handgun permits in the wake of a 2008 college shooting which killed 11.
But not all such atrocities have provoked this response.
Norway, where firearms restrictions were already robust, did not tighten its gun laws after the attacks in 2011 by Anders Behring Breivik.