Baldwin, who has been playing Trump on the comedy show since he took office, said the president “signals people” to become angry and bitter “and then the actions flow from there”.
“Nothing funny about tired Saturday Night Live on Fake News NBC!” he wrote on social media. “Question is, how do the Networks get away with these total Republican hit jobs without retribution? Likewise for many other shows? Very unfair and should be looked into. This is the real Collusion!”
He then added: “THE RIGGED AND CORRUPT MEDIA IS THE ENEMY OF THE PEOPLE!”
Baldwin first responded on Twitter, writing: “I wonder if a sitting President exhorting his followers that my role in a TV comedy qualifies me as an enemy of the people constitutes a threat to my safety and that of my family?”
He has since clarified the comment on the podcast The Dworkin Report, revealing that Trump’s message was indeed the first time he feared for his and his family’s safety.
“People would say to me early on, do you have any concerns about retaliation, not necessarily from the government or from Trump, but from his agitators?” Baldwin said.
“I always said not really, I didn’t really think that was something that was real, until now, when he made this comment about retribution and he thought SNL should be investigated.”
He continued: “Trump signals people, not necessarily what to do, but how to feel, and that’s the beginning. The beginning is you make people angry, the beginning is you make people agitated and bitter and then the actions flow from there.”
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The president has previously suggested that NBC, which airs Saturday Night Live, should have its station licenses challenged.
Trump's inner circle: Meet the members of the US president's cabinet
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Trump’s decision to circumvent lawmakers in his efforts to fulfil a campaign promise and build a wall across the US-Mexico Border has faced backlash from members of his own party, who called the move “a mistake”.
“I wish he wouldn’t have done it,” said Republican Senator Chuck Grassley.
Democrats also branded the national emergency as “fake” and unnecessary. Progressive newcomer Alexandria Ocasio-Cortez and Texas Democrat Joaquin Castro announced a new resolution that would rebuke the measure and could potentially block plans for the wall if enough Republicans were to support that move, leading to a foolproof majority.
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