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Donald Trump and administration officials have threatened CNN over what they said was its promotion of a new app that allows users to track and try to avoid Immigrations and Customs Enforcement agents.

Speaking to reporters in Florida on a trip to visit a new Ice detention center in the Everglades, dubbed “Alligator Alcatraz”, the homeland security secretary, Kristi Noem, said her department and the Department of Justice were looking at prosecuting CNN over its reporting on the app, called IceBlock.

“We’re working with Department of Justice to see if we can prosecute them,” Noem said, “because what they’re doing is actively encouraging people to avoid law enforcement activities and operations. We’re going to actually go after them and prosecute them. What they’re doing is illegal.”

Trump joined in, saying the news network – a frequent target of his ire – should also be prosecuted for what he said were “false reports on the attack on Iran”, referring to the leak of a Pentagon assessment that suggested US strikes on Iran’s nuclear facilities did not destroy the core components of the country’s nuclear program and had probably only set the program back by months.

CNN defended its reporting of the app through a spokesperson, saying:

This is an app that is publicly available to any iPhone user who wants to download it. There is nothing illegal about reporting the existence of this or any other app, nor does such reporting constitute promotion or other endorsement of the app by CNN.

Noem’s comments came hours after Tom Homan, Trump’s border czar, also criticized the news outlet for its reporting on the IceBlock app.

“It’s disgusting,” Homan said during an appearance on the rightwing commentator Benny Johnson’s internet show. “I can’t believe we live in a world where the men and women in law enforcement are the bad guys. It’s already a dangerous job.”

Homan had been asked about the app, which was created to report sightings of Ice agents in any given area. Software developer Joshua Aaron recently told CNN that he had launched the app “when I saw what was happening in this country”.

“I wanted to do something to fight back,” Aaron said, telling the network that the administration’s deportation efforts were, to him, reminiscent of Nazi Germany. “We’re literally watching history repeat itself,” Aaron said.

Homan also suggested CNN was complicit in putting federal law enforcement in danger.

“This is horrendous that a national media outlet would be out there trying to forecast law enforcement operations,” he said. “I think DoJ needs to look at this. They’re crossing that line.”

He added: “We need to send a strong message that we need to protect the law enforcement officers.”