WASHINGTON — President Obama’s rage about gun massacres, building for years, spilled out Thursday night as he acknowledged his own powerlessness to prevent another tragedy and pleaded with voters to force change themselves.

“So tonight, as those of us who are lucky enough to hug our kids a little closer are thinking about the families who aren’t so fortunate,” the president said in the James S. Brady Press Briefing Room, named for a man severely wounded by a would-be assassin’s bullet, “I’d ask the American people to think about how they can get our government to change these laws, and to save these lives and let these people grow up.”

Mr. Obama admitted that he was unable to do anything to prevent such tragedies by himself. And he did little to try to hide the anger and frustration that have deepened as he returns again and again to the White House lectern in the wake of a deadly mass shooting.