Dr Martin told how he had received a threatening letter in the wake of revelations by Taoiseach Enda Kenny that he had also received a threat – as tensions on the contentious issue look likely to continue to heighten.
He said he received the letter in the past week and reported it to gardai straight away.
Dr Martin said: "I have received also a threatening letter which says because of my views on abortion I should be careful when I go out on the streets.
"There are strange people around, I have no bullet-proof vest on. I have constantly said mature debate should be measured debate. The Catholic position is a very strong one about the equal right of mother and baby and that is the situation we have."
Dr Martin has reported the threat to gardai, who will now investigate the matter.
Dr Martin also said yesterday that people should be able to express their views "with conviction", but added that "extreme language" and personal attacks were not the way "we go forward".
He was responding to Taoiseach Enda Kenny's claim that he had been threatened with "revenge for Cloyne" in the abortion debate, a reference to Mr Kenny denouncing the Vatican in the wake of the Cloyne Report into clerical abuse.
The Government this week outlined plans to legislate and regulate for abortion in cases where there is a threat to the life of the mother – including the highly contentious issue of the threat of suicide.
Dr Martin – one of a number of bishops who attacked the Government's proposals to legislate for abortion – has called for a calm debate on the issue.
It comes after the four Catholic archbishops this week called for TDs to be given a free vote when abortion legislation comes before the Dail, which is expected to be early next summer.
Dr Martin repeated this call yesterday, but this has been firmly ruled out by Mr Kenny.
As revealed in the Irish Independent, the Taoiseach told his TDs "a messenger" had threatened him with "revenge for Cloyne".
He also told his Fine Gael colleagues he believes he will become a target for more abuse as relations between church and State deteriorate over the abortion row.
Mr Kenny said the message was passed to him earlier this week, but he did not say if it was in writing or said to his face, or who sent it.
Revenge
Some TDs took it that the archbishops' statement was the "revenge", but Dr Martin's spokeswoman insisted there was no connection whatsoever.
Puzzled TDs said Mr Kenny's claim was like something from a Dan Brown novel.
But Independent National University of Ireland (NUI) Senator Ronan Mullen criticised Mr Kenny for highlighting "the specifics of abusive correspondence" and said he was only giving "oxygen" to malcontents.
Mr Mullen said "a lack of civility on the part of individuals is not confined to one side or the other" of the abortion debate.
"Selectively drawing attention to abusive anti-abortion correspondence does a disservice to the tens of thousands of members of the pro-life movement who are sincere, respectful and well-intentioned," he added.
Communications Minister Pat Rabbitte said he was "taken aback by the vigour of the language" used by archbishops in their statement earlier this week.
He said he had "no objection at all" to the archbishops making their opinions known.
But added: "What I do not want to see is the clergy dictating to legislators how to legislate. But I have no objection to the bishops making their input."
Archbishop Martin said "nobody should be told by government that they have no right to speak".