On the train back to Connecticut, the relatives drafted a statement criticizing Mr. Christie, saying, “His refusal to meet with us is a cowardly political move, but his statement accusing us of ‘grandstanding’ and furthering ‘empty rhetoric’ is a blow to the memories of our children.” They drafted a new petition asking him to meet with them personally, and to explain the veto. The petition, they said, had tens of thousands of signatures within hours, and a #NotTrivial hashtag had taken root on Twitter.

“We have treated him, we have treated this issue, with nothing but respect,” said Mark Barden, whose son, Daniel, died at Sandy Hook. “We do not get into the shaming that a lot of folks do. But he started slinging the insults. We’re not going to insult him back, but we are going to expose his own words and make sure people know them — calling this a trivial measure when he’s talking about the lives of our children.”

The bill, passed in May in a Legislature controlled by Democrats, would have lowered the legal limit on magazine rounds to 10 from 15. Sandy Hook families and other gun control groups argue that it would save lives — 11 children escaped when the Newtown gunman stopped to reload. More children could have escaped, they argue, if he had been forced to stop sooner. The federal assault weapons ban included a ban on magazines higher than 10 rounds, but it expired in 2004.

“The one single component on a firearm that influences mortality more than anything else is the number of bullets you can load into it,” Mr. Barden said.

Polls show that New Jersey residents support the ban. But the move by Mr. Christie, a Republican with a high national profile, was not a surprise. Last year, he vetoed a ban on .50-caliber rifles though he had proposed a similar ban himself. He said the language was narrower in his bill, but critics accused him of pandering to gun owners’ groups, which can have disproportionate political sway, particularly in early primary and swing states. The governor is to campaign on behalf of other Republicans in New Hampshire and Iowa over the next few weeks.