COMMUNICATIONS Minister Pat Rabbitte has described a series of offensive tweets posted about Senator Ronan Mullen as "deplorable" and "offensive".
The tweets, many of which were written by musical director of 'The Late Late Show', Jim Sheridan, contained words and images mocking Mr Mullen.
He said they were "a very personal attack" on the senator, which "humiliated and ridiculed" him.
RTE confirmed it was looking into the matter.
Mr Sheridan has defended his tweets, saying they are "satire and a joke".
Days before Christmas, Mr Sheridan took part in a conversation on Twitter in which another user suggested that Mr Mullen be crucified with "rusty nails".
Mr Sheridan responded: "He'd be back in three days ... But we could have at least one great weekend without him appearing on TV or radio."
"Someone sent me a tweet which I took in good faith as a joke and was not a serious threat to Ronan Mullen. My response was to keep up the analogy about comparing him to Jesus," said Mr Sheridan.
One of his tweets depicts an image of the infant Jesus with the head of the senator superimposed on top. In another, the head of the politician is stuck onto the body of a man wearing nothing but swimming trunks and a large crucifix.
Mr Sheridan said that he parodied politicians from a range of parties and countries and did not wish to be seen as malicious.
He said in a statement: "Since the beginning of my participation on Twitter, I have been an outspoken advocate against cyberbullying and anonymous online threats. I would find the allegation of being a cyberbully untruthful and damaging."
But last night, Mr Rabbitte described the tweets as "dreadful and offensive" and said he could not see any humour in them. "I deplore this kind of communication from any source," he added.
Mr Mullen said it was of concern that "such virulent nastiness" would come from someone within RTE.
A spokesperson for RTE said: "We are discussing the tweets with him in relation to our social media guidelines."
RTE declined to confirm if it would be taking any action in relation to Mr Sheridan's tweets.