Preliminary tests on the substance in the envelope sent to Eric Trump's apartment yesterday indicated it was not hazardous, according to the officials, who were not authorised to disclose details of the threat and spoke to The Associated Press on condition of anonymity.
The handwritten letter was postmarked March 5 from Boston and referenced Donald Trump's presidential bid.
The letter said: "If your father does not drop out of the race, the next envelope won't be a fake." It was signed "X," according to one of the law enforcement officials, who had seen the letter.
Eric Trump, 32, is one of five children of businessman and Republican presidential front-runner Donald Trump. He has been campaigning for his father.
Donald Trump's representatives did not immediately respond to a request for comment.