The White House's Jay Carney went further than the president's comments on Monday in a memorial service for the Newtown victims to support senator Dianne Feinstein's proposed bill.
In addition to reinstating the ban on assault weapons that previously existed, Ms Feinstein wants to close a loophole in gun-show sales.
Mr Carney said: "It's clear that as a nation we haven't done enough to address the scourge of gun violence."
Mr Obama had said on Monday that America had to change its attitudes to prevent future gun tragedies.
It came on the day Cerberus Capital Management announced it was selling its stake in the manufacturer of one of Lanza's guns, a Bushmaster AR-15. It had invested $751.4 million (£462m) with Cerberus.
Lanza also used two handguns, a Glock and a Sig Sauer in Friday's shootings.
The private equity firm's move came after a major investor, California State Teachers' Retirement System, reviewed its links to Cerberus.
Gun retailers also began to feel the impact of the waves of revulsion felt by the nation over the child killings.
Dick's Sporting Goods pulled all guns from its store closest to Newtown and suspended the sale of certain semi-automatic rifles in its stores nationwide.
Walmart Stores took down an information website about semi-automatic Bushmaster rifles.
However, Money manager Vanguard Group Inc, the largest owner of gunmaker Smith Wesson Holding Corp, said it cannot operate its big index funds to meet what it called the "social concerns" of all shareholders.
Meanwhile, four people died in an apparent murder suicide in Colorado.
A man killed at least one other person and then himself, part of an apparent murder-suicide that left two men and two women dead.