WASHINGTON (Reuters) - President Barack Obama said on Monday that mass killings like the shooting rampage at a Sikh temple in Wisconsin were occurring with "too much regularity" and should prompt soul searching by all Americans, but he stopped short of calling for new gun-control laws.

"All of us are heart-broken by what happened," Obama told reporters at the White House a day after a gunman opened fire on Sikh worshippers preparing for religious services, killing six before he was shot dead by a police officer.

But when asked whether he would push for further gun-control measures in the wake of the shootings, Obama said only that he wanted to bring together leaders at all levels of American society to examine ways to curb gun violence.

That echoed his pledge last month in a speech in New Orleans to work broadly to "arrive at a consensus" on the contentious issue after a deadly Colorado shooting spree highlighted the problem in an election year.

But like his earlier comments, Obama offered no timetable or specifics for such discussions and did not call outright for tighter gun control laws.

Talk of reining in America's gun culture is considered politically risky for Obama, who is locked in a tight race against Republican challenger Mitt Romney for November election.

"All of us recognize that these kinds of terrible, tragic events are happening with too much regularity for us not to do some soul searching to examine additional ways that we can reduce violence," Obama said at an Oval Office ceremony to sign an unrelated bill.

But he added, "As I've already said, there are a lot of elements involved in it." The Democratic president has made a point of emphasizing his support for the U.S. Constitution's Second Amendment, which covers the right to bear arms.

White House spokesman Jay Carney reiterated, however, that Obama remained in favor of renewing an assault weapons ban but pointed out "there has been reluctance by Congress" to pass it.

Obama said the FBI was still investigating the temple shooting, but if it turned out it was ethnically motivated, the American people would "immediately recoil."

"It would be very important for us to reaffirm once again that in this country, regardless of what we look like, where we come from, who we worship, we are all one people," he said.

Police identified the Wisconsin gunman as Wade Michael Page, a 40-year-old U.S. Army veteran. A group that monitors extremists said he was a member of a racist skinhead band.

In a show of respect for the victims of the shooting in a Milwaukee suburb of Oak Creek, Obama ordered flags at all U.S. government facilities at home and abroad to be flown at half staff until sunset on Friday.

But in his appearance before reporters on Monday, he did not answer a question on whether he planned to travel to Wisconsin.