The Connacht-Ulster MEP, Ms Dana Rosemary Scallon, has challenged the Catholic bishops to explain how calling for a No vote conflicts with church teaching.
In a statement, she criticises the singling out of her by name by a number of bishops in the past week, and asks the bishops for clarification on how they can support protection of what they described as an abortifacient.
A spokesman for the MEP said three bishops were reported in the media naming her and describing her position as "misguided". He said Cardinal Connell had also said on RTÉ news that those voting No from a pro-life standpoint were "misguided", while her photograph was shown on the television to illustrate the report.
Her spokesman continued: "A lot of things are being done that are not right." Asked to specify, he said menacing phone calls and letters had been received by Ms Scallon's Galway office since she announced her opposition to the wording of the amendment, adding: "There have been irrational responses."
Ms Scallon said in her statement she had kept the bishops fully informed of her concerns from the first publication of the referendum proposals. She said she had recently requested a personal meeting with Cardinal Connell, but this was refused.
She said: "I welcome Cardinal Connell's statement that Catholics informed of the bishops' views on the issue were free in conscience to vote differently. If my position is in some way contrary to church teaching then let that issue be addressed and show me the contradiction, if it exists.
"My position remains the same as it has always been - that I uphold the dignity of life from the moment of conception to natural death, and in good conscience I cannot support the wording of the amendment."