On Aug. 3, 2019, a far-right gunman killed 23 people at a Walmart store in El Paso. Early the next morning, a man shot and killed nine people outside a bar in Dayton, Ohio. Both assailants used semiautomatic rifles.

At the White House the next day, Mr. Trump was so shaken by the weekend’s violence that he questioned aides about a specific potential solution and made clear he wanted to take action, according to three people present during the conversation.

“What are we going to do about assault rifles?” Mr. Trump asked.

“Not a damn thing,” Mick Mulvaney, his acting chief of staff, replied.

“Why?” Trump demanded.

“Because,” Mr. Mulvaney told him, “you would lose.”