Actor Alec Baldwin has taken to social media to mock Donald Trump, sharing a picture of himself on Instagram wearing a hat bearing the slogan 'Make America Great Again', written in Russian.

Baldwin's tweet came as Trump faces criticism for his reluctance to accept US intelligence information that claims Russia's alleged hack of the Democratic National Committee benefited him in the presidential election.

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The Saturday Night Live regular, whose impression of Trump has been slammed by the Republican himself, seems to be stepping up his Trump mockery, as he recently jokingly offered to perform at the president-elect's inauguration.

"I wanna perform at the inauguration. I wanna sing Highway to Hell," Baldwin tweeted on 23 December, sharing a video of the ACDC hit.

The actor has previously been derided by Trump for his impression of the president-elect, who tweeted on watching the now infamous Saturday Night Live skit: "Just tried watching Saturday Night Live - unwatchable! Totally biased, not funny and the Baldwin impersonation just can't get any worse. Sad."

Trump has not issued a response to Baldwin's latest tweet, but has recently engaged in a twitter spat with former California governor Arnold Schwarzenegger over the ratings on The Celebrity Apprentice, a show on which Trump is an executive producer.

In a series of tweets, Trump wrote: Wow, the ratings are in and Arnold Schwarzenegger got "swamped" (or destroyed) by comparison to the ratings machine, DJT.

"So much for being a movie star-and that was season 1 compared to season 14. Now compare him to my season 1. But who cares, he supported Kasich & Hillary."

Schwarzenegger tweeted in response: ""I wish you the best of luck and I hope you'll work for ALL of the American people as aggressively as you worked for your ratings."

His twitter spats had previously prompted concern from some people within the GOP, who feared he would continue using twitter to issue controversial statements.

Donald Trump