A government-commissioned report published on Tuesday found an "appalling" mortality rate of around 15% among children born at the homes, reflecting brutal living conditions.
"On behalf of the government, the state and its citizens, I apologize for the profound generational wrong visited upon Irish mothers and their children who ended up in a Mother and Baby Home or a County Home," Martin told parliament.
"I apologize for the shame and stigma which they were subjected to and which, for some, remains a burden to this day," Martin said. "The state failed you."
The report detailed how many infants were taken from mothers and sent overseas to be adopted, while a number of children were vaccinated without consent.
Anonymous testimony from residents compared the institutions to prisons where they were verbally abused by nuns, while women suffered through traumatic labors without any pain relief.
Relatives have alleged babies were mistreated because they were born to unmarried mothers who, like their children, were seen as a stain on Ireland's image as a devout Catholic nation.