Heart-rending funerals were held Monday for two six-year-old boys, as America began to say farewell to the 20 children slain in a school shooting that has sparked calls for new gun laws.

The first burials, held under raw, wet skies, were of a pair of boys who were among those shot in Sandy Hook Elementary School, in Newtown, Connecticut. On Tuesday, the first of the girls, also aged six, was to be laid to rest.

In all, on Friday, the gunman slaughtered 20 children aged between six and seven, six adults working at the school and his own mother, before turning one of his arsenal of high-powered firearms on himself.

"You see little coffins and your heart has to ache," said state governor Dannel Malloy.

The family of six-year-old Jack Pinto gathered at a funeral home in a century-old building in the center of the Connecticut town. Some 20 children of different ages came to bid him farewell.

Jack Wellman, an eighth-grader who helped coach Jack in wrestling, said teammates placed their sports medals in his coffin.

"He was an excellent kid," Wellman said at a nearby deli afterwards.

Another well-wisher was overwhelmed. "I just cannot describe it, it was sad. The message was just comforting," she said. "Our hearts are heavy."

All schools in this prosperous and picturesque town northeast of New York City were shut until at least Tuesday and the blood-spattered elementary school itself was to remain a closed crime scene indefinitely, authorities said.

"Healing is still going on," Newtown police Lieutenant George Sinko said.

In the nearby town of Ridgefield, reports of a suspicious person prompted the brief lockdown and deployment of police Monday at schools, in a sign of the jitters in the United States in the wake of the killings.

For Newtown, a quiet suburban community where the 20-year-old killer lived with his well-off mother, the start of funerals did nothing to heal wounds.

But the crime, in which the shooter carried a high-powered, military style rifle and two handguns, may have spurred change in the political landscape regarding rules on weapons ownership.

The Senate held a moment's silence in Washington, as several Democratic lawmakers who had previously opposed gun control changed their stance.

Late Sunday, President Barack Obama joined a vigil in Newtown and pledged to work for an end to mass shootings, which have now become a regular event in the United States -- with half-a-dozen massacres since Obama took office.

"These tragedies must end," Obama said, appearing to commit himself to a push for reform in his second White House term, possibly by urging the restoration of a federal ban on assault weapons like the one used in Newtown.

But hopes that the president might have a plan to address the issue were dashed on Monday, when his spokesman Jay Carney said: "I don't have a specific agenda to announce to you today."

Voters meanwhile rushed to sign an online petition on the White House website calling for tougher gun laws -- 158,000 signed in three days, the fastest ever burst of support in the site's history.

Democratic Senator Dianne Feinstein of California promised to introduce a bill to ban assault weapons on the first day of the next Congress, January 3.

And on Monday, Senator Joe Lieberman of Connecticut called for a broad commission that could bring opponents on the issue together to discuss curbing gun deaths.

Each year, more than 31,000 Americans die from gunshots, most of them self-inflicted, but more than 11,000 in homicides -- five times as many as the death toll for US troops during an entire decade of conflict in Afghanistan.

"We've got to bring everybody to the table, including the gun manufacturers and the gun rights groups and the entertainment industry and just regular people," Lieberman, a Democrat-turned-independent, told Fox News.

But with gun ownership protected by the US constitution and firearms deeply ingrained in American culture, attempts to restrict access have long been seen as a vote-losing proposition.

The full picture of the horror and heroism in the school, where the shooter, Adam Lanza, sprayed bullets into two rooms, is starting to emerge.

The husband of Dawn Hochsprung, the slain school principal, said she had told others around her to hide. Then she "and at least one other teacher went out and actually tried to subdue the killer."

"I don't know where that comes from. Dawn was 5'2"," he said.

"Dawn put herself in jeopardy and I have been angry about that, angry -- until just now, when I met two women that she told to go under shelter while she actually confronted the gunman."

One of the teachers, Janet Balmer, told CNN how when she heard gunshots, she followed the lockdown routine the school had recently practiced, then tried to act in front of her five-year-old charges as if all was well.

"We sat in the cubby away from the door so no one could see us, read them a story and talked to them," she said.

After agonizing minutes, police knocked at the door and told the children to leave and to "cover their eyes" to avoid being exposed to the gore.

No information about a possible motive, or whether Lanza had any diagnosed mental condition, has emerged. He is believed to have shot his mother in their house before going to the school.

Newtown was the second deadliest school shooting in US history after the Virginia Tech massacre in 2007, in which South Korean student Seung-Hui Cho shot and killed 32 people and wounded 17 others before taking his own life.