Michael Bloomberg, the mayor of New York, has called on Barack Obama and Mitt Romney to address gun control in the wake of the killings of 12 people at a Colorado theater.

Bloomberg criticised the presidential candidates for offering sympathy for the victims but avoiding the thorny political issue of America's loose gun laws. He said in a radio interview that "soothing words are nice" but not enough.

"Maybe it's time the two people who want to be president of the United States stand up and tell us what they're going to do about it, because this is obviously a problem across the country. And everybody always says: Isn't it tragic?" he said.

"There's so many murders with guns every day It's just gotta stop. And instead of these two people, President Obama and Governor Romney talking in broad things about they want to make the world a better place. OK, tell us how. And this is a problem. No matter where you stand on the Second Amendment, no matter where you stand on guns, we have a right to hear from both of them, concretely, not just in generalities, specifically, what are they going to do about guns?"

Obama responded to the shootings by pulling his campaign adverts from Colorado television stations and calling off a political rally in Florida where he limited himself to moving remarks in sympathy with the victims.

"Now, even as we learn how this happened and who's responsible, we may never understand what leads anybody to terrorise their fellow human beings like this. Such violence, such evil is senseless. It's beyond reason. But while we will never know fully what causes somebody to take the life of another, we do know what makes life worth living. The people we lost in Aurora loved and they were loved. They were mothers and fathers; they were husbands and wives; sisters and brothers; sons and daughters, friends and neighbours. They had hopes for the future and they had dreams that were not yet fulfilled," Obama said to strong applause.

"If there's anything to take away from this tragedy it's the reminder that life is very fragile. Our time here is limited and it is precious. And what matters at the end of the day is not the small things, it's not the trivial things, which so often consume us and our daily lives. Ultimately, it's how we choose to treat one another and how we love one another."

But Obama made no mention of gun control nor questioned how it is that a person who he describes as "evil" was able to obtain weapons. Neither did Romney in his response to the shooting.

"We are praying for the families and loved ones of the victims during this time of deep shock and immense grief. We expect that the person responsible for this terrible crime will be quickly brought to justice," said the Republican candidate.

Bloomberg's demand was backed by the Brady Center to Prevent Gun Violence, named after the White House press secretary wounded in an assassination attempt against President Ronald Reagan.

Daniel Vice, the group's senior attorney, accused Obama and Romney of cowardice on the issue.

"If they don't speak out soon, very soon, then that will be shameful," he said. "Mitt Romney, when he was governor signed an assault weapons ban into law. President Obama has said in the past that he supports strong guns laws but he has done nothing to improve our gun laws and actually has gone backward. We do see far too much cowardice on the part of our political leaders but Americans are angry and they are demanding change."

National opinion polls show that, if anything, there is growing support for easing gun regulation. Two decades ago, about 70% of Americans favoured stricter firearms control, according to Gallup. Today more than half support less regulation. It seems that with each new massacre - Columbine in 1999, Virginia Tech, Tucson – support for controls fell.

Last year, in the wake of the shooting of Congresswoman Gabrielle Giffords and others in Arizona, a Pew Research Center poll showed a small spike in support of greater gun control but the drift has largely been the other way.

Vice said that does not reflect the views of Americans on the specifics of gun control.

"It all depends on the poll," he said. "People don't realise how weak our gun laws are. When you ask them specifics – should we have background checks? Should we ban assault weapons? – there's overwhelming support for those laws."