Martin said he would make a formal apology on behalf of the state in Dáil Éireann, Ireland's lower house of parliament, on Wednesday.
"Irish society demanded that many unmarried women would have their babies in secret".
Government records show that the mortality rate for children at the homes where tens of thousands of women, including rape victims, were sent to give birth, was often more than five times that of those born to married parents.
"But certainly I wasn't aware that the report itself had been leaked", said the Taoiseach.
The investigation found that the high level of infant mortality at the Tuam Children's Home did not feature at meetings Galway County Council meetings, though the home was under the control of the local authority which held its meetings there.
The greatest number of admissions was in the 1960s and early 1970s.
Numerous women received little or no ante-natal care. Separately, Labour Party leader Alan Kelly called on the Taoiseach to postpone his State apology to allow people affected by the report read it first. "One hard truth in all of this, is that all of society was complicit in it", he added.
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"We especially want to recognise and accept today that so many women who were shunned and shamed by society did not find the support and level of care they needed and deserved at such a awful and painful time in their lives", a statement from the order read.
"We had a completely warped attitude to sexuality and intimacy". We embraced a perverse religious morality and control which was so damaging ...
"The report makes clear that for decades, Ireland had a stifling, oppressive and brutally misogynistic culture", said Ireland's Children's Minister, Roderic O'Gorman.
The government pledged to pursue the commission's recommendations, which include providing financial compensation and medical support for those former residents still alive.
The Commission of Investigation's final report into Mother and Baby Homes will be brought to Cabinet later.
In the years before 1960, it said, mother-and-baby homes did not save the lives of "illegitimate" children - instead, they significantly reduced prospects of their survival.
The homes became an worldwide news story in 2014 after significant human remains were found in the grounds of a former home in Tuam, County Galway.
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The remains of 802 children, from newborns to three-year-olds, were buried between 1925 and 1961 in just one of the homes, a 2017 interim report found.
A national memorial and records centre related to institutional trauma during the 20th century will also be developed.
Meanwhile, women of the period who gave birth outside marriage were "subject to particularly harsh treatment" at the hands of families and partners, backed by both Church and state.
The report is expected to be the last in a series to shine a light on a very different and very clerical Ireland.
He described the leaks as a further slap in the face for the survivors and their families, who, unlike parts of the media, were not being given enough time to get an advance view of the contents of the report, due to be published this week.
Survivors of the homes also expressed their anger.
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The Fulham boss criticised the decision, with their game against Chelsea scheduled for Friday also put back 24 hours. "The biggest impact is to have matches postponed ", he added.