However 17% of people who responded said they were on the middle ground.
The Irish Times/MRBI poll found that 44 percent would vote to repeal an amendment to the constitution that enshrines the equal right to life of the mother and her unborn child, with 32 percent opposed.
The Together For Yes campaign claimed the poll shows "strong support for change amongst the Irish public".
Among those who are undecided, the poll found that 31% are leaning towards a Yes vote and 23% are leaning towards a No vote. The remainder stated that they were not leaning in either direction.
In a letter written ahead of the 25th May referendum on repealing the eighth amendment, the group of 26 psychiatrists said it was "dishonest" to justify a change in the law as healthcare.
If the undecideds are excluded from the overall figures, the Yes side now leads by 58% to 42%.
Dublin is the most pro-repeal county in the country, with 68% of voters in favour of a yes vote and 32% in favour of a No, when the undecided figures are removed.
Ulster and Connacht show the tightest margins with 51% of those surveyed saying they will likely be voting "Yes", while 49% will vote "No".
"As consultant psychiatrists, it is the so-called "mental health" ground that particularly concerns us because we know from official United Kingdom statistics that 97pc of the nearly 200,000 abortions which occur annually in the United Kingdom, take place under the "mental health" ground".
The poll was conducted on 15 and 16 May, and saw the face-to-face participation of 1,200 eligible voters across all constituencies.