A tearful President Barack Obama says US leaders must "take meaningful action" regardless of politics in response to the mass shooting at a Connecticut elementary school.

The president teared up, at times using an index finger to wipe at the corner of his eyes, as he addressed the nation from the White House.

He also paused repeatedly as he struggled to keep his composure while speaking of the children ages 5 to 10 who had died and the life milestones they now would miss.

He said, quote, "Our hearts are broken."

Shortly before speaking, Obama ordered that US flags be flown at half-staff on public grounds through Tuesday.