He also announced 23 steps he intends to take immediately without congressional approval. These include improving the existing system for background checks, lifting the ban on federal research on gun violence, putting more counselors and "resource officers" in schools and better access to mental health services.
Obama signed three of the measures at the ceremony.
Obama, who has called the day of the Newtown massacre the worst of his presidency, looked down into the audience and addressed the parents of one of the Sandy Hook victims, Grace McDonald, 7, saying he had hung one of her paintings in his private study.
"Every time I look at that painting, I think about Grace, and I think about the life that she lived and the life that lay ahead of her, and most of all I think about how when it comes to protecting the most vulnerable among us, we must act now," he said.
As he announced the gun measures, Obama was accompanied by four children chosen from among those who sent letters to him about gun violence and school safety. "We should learn from what happened at Sandy Hook. I feel really bad," 8-year-old Grant Fritz wrote, in a portion Obama read from the podium.
The most contentious piece of the package is Obama's call for a renewed ban on military-style assault weapons, a move that is unlikely to win approval because Republicans who control the House of Representatives are expected to oppose it.
The Newtown gunman, 20-year-old Adam Lanza, used a Bushmaster AR-15 type assault rifle to shoot his victims, most of them 6- and 7-year-olds, before killing himself.
Law enforcement experts have noted, however, that the tighter background checks that Obama is proposing would not have prevented the Connecticut school massacre because the gunman's weapon was purchased legally by his mother.