Representative Seth Moulton, Democrat of Massachusetts, is facing a barrage of criticism and protest in his deep-blue state for suggesting that his party’s struggles in this month’s election could be traced to its support for allowing transgender girls to play in girls’ sports.

Mr. Moulton’s campaign manager resigned in protest. The Democratic governor of Massachusetts rebuked him. And the chair of the political science department at Tufts University threatened to block his students from interning in Mr. Moulton’s office.

A rally has been scheduled for Sunday in Salem, Mass., Mr. Moulton’s hometown, aimed at standing with the transgender community, said Kyle Davis, a Democrat and a Salem city councilor who has called on the congressman to resign.

“We’re certainly rejecting the narrative that trans people are to be scapegoated or fear-mongered against,” Mr. Davis said.

In the interview that touched off the furor, given recently to The New York Times, Mr. Moulton said Democrats had spent “too much time trying not to offend anyone.”

“I have two little girls. I don’t want them getting run over on a playing field by a male or formerly male athlete,” he said. “But as a Democrat, I’m supposed to be afraid to say that.”