Actor Alec Baldwin has responded to Donald Trump’s furious response to his Saturday Night Live (SNL) parody by asking whether the US President’s tweets constitute a threat to him and his family.

Mr Trump on Monday morning (Australian time) accused popular SNL of being an “ENEMY OF THE PEOPLE” in a furious Twitter attack over its latest episode in which Baldwin satirised the President declaring a national emergency at the southern US border.

“Wall works, wall makes safe,” Baldwin’s President Trump said in the show’s opening.

“You don’t have to be smart to understand that – in fact, it’s even easier to understand if you’re not that smart,” he declares.

Minutes later, he expanded his anger to include the media at large, tweeting: “THE RIGGED AND CORRUPT MEDIA IS THE ENEMY OF THE PEOPLE!”

Baldwin responded Monday morning by questioning whether “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?”

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?

— AlecBaldwin(HABF) (@AlecBaldwin) February 18, 2019

Political parodies are by no means new, especially by the long-running SNL.

Previous US leaders, including the late George HW Bush, Gerald Ford and Barack Obama have responded with good grace to lampooning by the show’s cast members.

Mr Trump’s response to the show came in sharp contrast to that of Democratic Senate Minority Leader Chuck Schumer who also took to Twitter to respond to his portrayal on the latest episode of the show.

Good impersonation, @NBCSNL. But got one thing wrong. I use a flip phone! https://t.co/R7bmYqfNKk pic.twitter.com/RPbwegbdCK

— Chuck Schumer (@SenSchumer) February 17, 2019

Mr Schumer, played by SNL cast member Alex Moffat, was shown gloating over the recent US budget deal.

The Senator shortly after tweeted a photo of the segment, in which Moffat was holding up a smartphone, saying: “Good impersonation, SNL. But got one thing wrong. I use a flip phone!”