A Rochester, New York, man says Homeland Security Investigations agents tracked him down at his home and later at an airport hotel about five months after he sent a scathing email to then-acting ICE Director Todd Lyons, in a case that civil liberties advocates say reflects an effort by the Department of Homeland Security to intimidate government critics.

David Streever, 45, was vacationing in Finland with his 7-year-old daughter last week when his doorbell camera captured two law enforcement officers in blue jackets waiting on his porch, according to an NPR report published Wednesday. His wife, the Rev. Hilary Streever, 43, an Episcopal priest, said the agents told her they were investigating “an email he may or may not have sent threatening” Mr. Lyons.

The agents left Ms. Streever a form warning that Mr. Streever “may be in violation of federal law” and citing statutes that make it a crime to threaten federal officials, NPR reported. Ms. Streever told the outlet her husband was traveling and would return that Friday.

Mr. Streever told NPR he was baffled by the visit.

“I’ve never made a threat against anyone. I’m not a violent person,” he said.

He said the only email he recalled sending to Mr. Lyons’ government address was a Jan. 26 message he wrote after federal immigration officers fatally shot two people during operations in Minneapolis, Renee Good and Alex Pretti. In that email, Mr. Streever compared Mr. Lyons to a Nazi official and predicted his eventual downfall, according to a copy reviewed by NPR.

The department issued a statement saying ICE “investigates all credible threats towards its employees and officers, including threats to the ICE Director,” and does not comment on ongoing investigations.

The Streevers later learned that the same two agents had visited a poll worker in Syracuse, Paigelynne Gonyea, earlier the same day over an Instagram post, presenting her with a similar warning form. Civil liberties groups say the two cases are the first they know of in which agents left a form for the recipient to sign.

Adam Steinbaugh, an attorney with the Foundation for Individual Rights and Expression, said the pursuit of Mr. Streever went beyond the bounds of legitimate investigation, calling it “clearly out of line.” He said the First Amendment protects the right of Americans to criticize the government, even harshly, and does not permit federal agents to pursue and confront critics over that speech.

Mr. Streever says the case escalated further after he landed at John F. Kennedy International Airport on his way home. Within hours, he says, a third HSI agent located him at the airport hotel where he was staying and left a business card at the front desk. Mr. Streever said he had not disclosed the hotel to anyone, including his wife, and DHS has not explained how the agent found him. Nathan Freed Wessler, deputy director of the ACLU’s Speech, Privacy and Technology Project, said the tactics used could have involved surveillance cameras, cellphone location data or credit card records, and that the episode “sure looks like a serious issue” under the Fourth and First Amendments.

Jeramie Scott, senior counsel at the Electronic Privacy Information Center, questioned why federal resources were devoted to tracking a private citizen over a months-old email, saying the effort appeared “more geared towards intimidation than actually any type of reasonable use of law enforcement resources.”

Mr. Streever ultimately decided not to call the agents back and instead went public with his account, saying the pursuit made him feel his original email had mattered more than he expected.