It came after an inquiry found women and girls subjected to harsh discipline, appalling conditions and unpaid work in the institutions were sent there by the state.
Taoiseach Enda Kenny expressed his sympathies to survivors and the families of those who have died.
The laundries, run by Catholic nuns, have been accused of treating inmates like "slaves", imposing a regime of fear and prayer on girls sometimes put in their care for simply falling pregnant outside marriage.
Irish governments had in the past denied blame, claiming the laundries were private institutions. But a 1000-page report published yesterday concludes there was significant state involvement, with one in four inmates sent there through various arms of government.
Scots film-maker Peter Mullan dug up the shameful period of Irish history in his award-winning, but controversial 2003 movie, The Magdalene Sisters which used a disused convent in Dumfries as its main location.
The film was condemned by the Catholic Church and in Italy screenings were picketed by priests. Despite this the film was a huge hit in both Italy and Ireland, historically two of the most devoutly Catholic nations in Europe.
Groups representing survivors of the Magdalene laundries – named after Mary Magdalene, the "fallen woman" of the Gospels – asked Mr Kenny to apologise on behalf of the state and wanted a compensation scheme to be established.
Mr Kenny said the laundries had operated in a "harsh and uncompromising Ireland", but he did not offer any financial compensation to survivors.
He told parliament: "To those residents who went through the Magdalene Laundries in a variety of ways – 26% of the time from state involvement – I am sorry for those people they lived in that kind of environment.
"It's not a single issue story. Those residents, all 10,000, arrived in the Magdalene Laundries through a variety of circumstances and for a variety of reasons – not the least of which was destitution and poverty."
The laundries put about 10,000 women and girls, some as young as nine, through a tough, uncompromising regime from the foundation of the Irish state in 1922 until 1996.
The report's findings follow investigations into clerical sex abuse and state-abetted cover-ups that have shattered the authority of the Catholic Church in Ireland and rocked its reputation worldwide.
The report – compiled by an inter-departmental committee established in 2011 – said: "Many of the women who met with the committee experienced the laundries as lonely and frightening places. For too long, they have been and have felt forgotten. None of us can imagine the confusion and fear experienced by these young girls, in many cases little more than children, on entering the laundries – not knowing where they were, feeling abandoned."
The inquiry chaired by Senator Martin McAleese found 2124 of those detained in the institutions were sent by the authorities.
Girls considered troubled or what were then called fallen women were sent there and did unpaid manual work.
In 2011, the UN Committee Against Torture called on the Irish government to set up an inquiry into the treatment of thousands of women and girls.