The White House said Monday it so far has "no specific agenda" to announce on preventing shooting massacres, as a clamor grew among Democrats and in the media for action on tighter gun controls.

President Barack Obama promised victims' families at a vigil Sunday for 26 people including schoolchildren killed in Connecticut on Friday that he would use the power of his office to try to end a rash of mass killings.

But the White House said it had yet to frame an approach, adding that Obama would engage Americans in the "coming weeks" on the way forward, as America tries to process the horror and shock of the Newtown shootings.

"I don't have a series of proposals to present to you," White House spokesman Jay Carney said, when pressed by reporters to explain what the president had meant during his tender eulogy for the slain children.

"I don't have a specific agenda to announce to you today. I will simply point you to what the president said last night about moving forward in the coming weeks. I would look for him to do that."

Carney did say that Obama still backs an extension by Congress of a ban on assault weapons, which lapsed in 2004, and could cover the kind of semi-automatic rifle used by gunman Adam Lanza in Newtown.

He described the Newtown slaughter as "exceptional in its horrendousness" and said that the answer to halting similar killings was "complex" and required more than gun laws and legislation.

That could be a hint that Obama will pursue attempts to broaden mental health coverage alongside new gun laws, amid concerns that people with unstable psychological conditions find it too easy to get guns.

Despite Obama's urgency in his speech on Sunday night, in which he warned America had not done its duty to protect its children, Carney declined to rank the priority gun control would hold in the president's second term.

In New York however, mayor Michael Bloomberg demanded immediate action to limit the approximately 30,000 deaths caused by firearms in America every year, according to the Centers for Disease Control and Prevention.

"Last night, the president said he would use whatever powers his office holds to address this violence. It is critical that he do so," Bloomberg said.

"Words alone cannot heal our nation, only action can do that," he said, urging Congress to impose a criminal background check for all gun sales, to ban assault rifles and high-capacity magazines and make gun trafficking a felony.

He also called on Obama to use his executive powers to require the federal government to send all necessary records on felons, domestic abusers and the mentally ill to the national criminal background check system.

"The president, with a simple stroke of his pen ... can assure the federal government of compliance with this provision."

Back in Washington, there were signs of movement on Capitol Hill.

Democratic Senator Joe Manchin, from conservative West Virginia, who once blasted away at a copy of proposed global warming legislation with a gun in a political ad, also seemed to sense a shift.

"Never before have we seen our babies slaughtered," he said on MSNBC, sketching over the fact that thousands of US kids die in gun violence.

Manchin, a hunter with an 'A' rating from the National Rifle Association gun lobby -- a measure of his pro-firearm voting record -- suggested a renewal of the assault weapons ban.

Senate Democratic majority leader Harry Reid, who has a reputation as a pro-gun politician, said lawmakers will this week begin debate how to "change laws and culture."

Reid did not mention outright whether the chamber would consider new legislation to ban certain assault weapons and high-capacity magazines, as has been proposed by prominent Democrat Dianne Feinstein.

Senior Republicans bemoaned the tragedy, but were less keen to talk gun control.