In a tweet of his own, Samuelsen said that Trump should “rein it in, focus on the fight for freedom and show respect for the office of president."
Samuelsen said that the clip was undignified and reflected a lack of respect for the office of president.
“It is important to remember that this is a president and not just any old Mr. Donald,” Samuelsen told news agency Ritzau.
“It is inappropriate to discuss things by throwing around insults or in this case a video that implies that you want to assault the free press. It is unfit behaviour for a president,” the foreign minister added.
Samuelsen said that he was concerned that the office of president was being undermined by Trump.
“In the last few days there have been some incredible tweets from Trump. It is not what you would expect from an American president. He is the leader of the world, and we should have confidence in his ability to hold that office,” he said.
The video clip posted by Trump originates from a ten-year-old wrestling TV show, on which Trump appeared as a celebrity guest.
The censure from Samuelsen is not the first time the Liberal Alliance party leader has openly criticised Trump - an act otherwise seen as rare in Danish politics.
“It is important for a president to rise above mudslinging and yelling on social media. He says things as they are, so I'm sure he can also take someone saying he should rein it in. That is what I'm doing,” Samuelsen said.
The foreign minister added that he did not see any reason for Prime Minister Lars Løkke Rasmussen to pass his message on to Trump.
Not all Danish politicians agreed with Samuelsen's criticism of the American president.
Søren Espersen, foreign policy spokesperson with the populist Danish People's Party (DF), a parliamentary ally of Samuelsen's Liberal Alliance, said that Rasmussen should ban his ministers from speaking openly on such topics.
“It think Anders Samuelsen should stop tweeting. And I think Løkke [Rasmussen] should tell all his ministers that the party's over. We don't tweet any more, particularly – and this is the serious matter in this case – concerning our relations with other countries. It is also significant for the perception of Denmark around the world that this is being sent by the foreign minister,” he told newspaper Politiken.
Espersen was himself critical of Trump's tweet, calling it “completely aggressive, childish and ridiculous”.
But the DF MP told Politiken that Samuelsen should have expressed his opinion via normal diplomatic channels.
“… just because this is outlandish from Trump, doesn't mean we should be outlandish too,” he said.
Espersen's party colleague Kenneth Kristensen Berth – one of the few Danish politicians to openly support Trump prior to his election in November 2016 – appeared not to be following Espersen's advice on social media use.
Berth responded to Samuelsen's tweet by telling him to concentrate on maintaining a good relationship with the US, before posting a separate tweet to a similar effect in English.
“Anders Samuelsen should really pull himself together now and find something worthwhile to do other than critiizing [sic.] Donald Trump,” Berth wrote.