US President Barack Obama has met senior officials to discuss how to respond to Friday's school shootings in Newtown, Connecticut, in which 20 children and six adults died.
The White House said curbing gun violence was a "complex" problem that required a comprehensive solution.
On Sunday Mr Obama told Newtown residents he would do everything in his power to prevent further tragedies.
The first two funerals of victims of the shooting were held on Monday.
Sandy Hook school pupils Noah Pozner and Jack Pinto, both aged six, were buried, and other victims' funerals will be held throughout the week.
The town has been removing Christmas decorations in mourning.
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The Sandy Hook gunman was named as Adam Lanza, who took his own life at the end of a killing spree that began with him shooting dead his own mother.
On Monday Mr Obama met Vice President Joe Biden, Education Secretary Arne Duncan, Attorney General Eric Holder, and Health and Human Services Secretary Kathleen Sebelius to discuss proposals aimed at reducing gun violence.
Mr Biden will be put in charge of the initiative, the Washington Post said quoting unnamed sources close to the government.
Earlier, White House spokesman Jay Carney said tighter gun control laws were part of the answer to violence in the US.
"It's a complex problem that will require a complex solution," Mr Carney said. "No single piece of legislation, no single action will fully address the problem."
He added that the president supported reinstating an assault weapons ban that expired in 2004.
Correspondents say Democrats have been reluctant to pursue gun control legislation, but that there are signs that fear could be abating, with two pro-gun senators calling for changes.
Mark Warner and Joe Manchin, who have "A" ratings from the National Rifle Association (NRA), now say action is needed after the massacre.
West Virginia Senator Mr Manchin told US network MSNBC on Monday that it was time to "move beyond rhetoric".
Mr Manchin, a gun owner and frequent hunter, said: "I don't know anyone in the sporting or hunting arena that goes out with an assault rifle."
Virginia Senator Mark Warner said that the "status quo isn't acceptable" and called for "rational gun control".
Mr Warner said he had been approached repeatedly over the weekend as people began to seek answers and solutions.
California Senator Dianne Feinstein, a long-time advocate for gun regulations, said on Sunday she would introduce assault weapons ban legislation in the beginning of the next congressional session.
On Sunday President Barack Obama told residents at a vigil in Newtown the US must do more to protect its children.
"We can't tolerate this any more," Mr Obama said. "These tragedies must end and to end them we must change."