The row has also threatened the survival of the Irish Daily Star in its current guise.
The tabloid is jointly owned by INM and Northern & Shell. Yesterday Northern & Shell disowned its Irish operation -- and threatened to close down the joint venture. Its chairman Richard Desmond said: "I am very angry at the decision to publish these photographs and am taking immediate steps to close down the joint venture."
Last night Joe Webb, chief executive of INM (Ireland) and a director of Independent Star, said: "This was a poor decision. These pictures should not have been published. I understand the anger that many Irish citizens feel at the offence caused to the British Royal family, especially in the light of the visit of Queen Elizabeth last year.
"That visit was an important culmination of the work of the Peace Process. Since then Ireland has regarded the Queen and her family in the warmest light. Kate Middleton is a member of her family -- and on behalf of INM, I wish to offer her my deepest apologies.
"We have noted Richard Desmond's statement and we will be launching an internal inquiry to ensure there will never be a repeat of this breach of decency. However, we will be doing everything in our power to safeguard the 70 jobs at the Irish Daily Star."
Northern & Shell said they were consulting their lawyers "as a matter of urgency over what we believe to be a serious breach of their contract". And the editor of the Daily Star Sunday in Britain also condemned the publication.
Gareth Morgan said: "We are absolutely horrified here in the office. I am not just talking on behalf of the Daily Star Sunday but the four other responsible titles in Northern & Shell. This has no merit as an editorial decision. This has no merit morally. Frankly, it's a morally horrible decision," he added.
In a statement issued last night, INM said: "Independent News and Media believe that republishing pictures of the Duke and Duchess of Cambridge was regrettable and in poor taste. INM had no prior knowledge of the decision."
News of the images caused an avalanche of online traffic trying to access the newspaper's website, which promptly crashed. The Royal couple were said to be "hurt, shocked, furious and disgusted" by the Dublin-based newspaper's decision.
But the Irish managing director and former editor of the Irish Daily Star, Ger Colleran, stoutly defended the publication of the images.
"What we do in the Irish Daily Star is to produce an Irish newspaper for an Irish audience. The photographs of images taken from the magazine were not printed in our Belfast edition and there were two reasons for that -- sensitivity to our British partners, Express Newspapers, and a slightly different legal regime," he said.
"The issue here is that one is somewhat surprised about the furore that's been created, particularly in a British media that gave freedom of speech to the world and is rightly called the Mother of Parliaments, underwritten by freedom of expression and a free press," said Mr Colleran.
Chairman of the Fine Gael party, Charlie Flanagan, said the decision to publish the pictures was a "disgrace". He tweeted: "Irish Daily Star disgraces itself yet again by now publishing Kate photos. Neither shame nor standards."
The Irish Daily Star is a joint venture between Express Newspapers, owned by British company Northern & Shell -- publisher of the UK Daily Star -- and Independent News and Media.
And there was the threat of an unprecedented High Court legal action taken by the British Royal family against the Dublin-based newspaper after Buckingham Palace branded the double-page spread in yesterday's edition of the tabloid as "motivated by greed".
Legal experts last night told the Sunday Independent that the Royal family -- who indicated through a spokeswoman that they are considering legal action -- could issue proceedings under Irish privacy laws over the printing of pages in the Star taken from the French magazine Closer, which originally published the series of photographs on Friday.
Prince William and Kate Middleton have already launched a lawsuit in France to prevent the €1m sale of the intimate pictures, taken of the couple by a photographer while they were holidaying in a private chateau in Provence.
A spokeswoman for the Royal couple said yesterday: "There can be no motivation for this action other than greed."
Following the publication of the pictures in Closer on Friday, St James's Palace said: "Their Royal highnesses have been hugely saddened to learn that a French publication and a photographer have invaded their privacy.
"The incident is reminiscent of the worst excesses of the press and paparazzi during the life of Diana, Princess of Wales, and all the more upsetting to the Duke and Duchess for being so.
In an unrepentant BBC interview, Irish Daily Star editor Mick O'Kane defended publication of the images, saying: "The Duchess would be no different to any other celeb pics we would get in, for example, Rihanna or Lady Gaga.
"She's not the future queen of Ireland, so really the only place this is causing fury seems to be in the UK.
"She's one of the most photographed people in the world, and she decides to partially disrobe on a balcony where it can be seen from a public road and she's stunned now, or the palace are annoyed, that people are interested in this. Of course people are going to be interested in this," he said.
A spokesman for the Minister for Communications, Pat Rabbitte, said he had no comment to make yesterday.
The British Embassy in Dublin also declined to comment.
The series of pictures were taken by an unidentified paparazzi photographer who staked out the property from a spot about 700 yards away.
The failure of the security team to protect the couple from intrusion was highlighted last night when another photographer told The Sunday Telegraph of the ease with which she had taken "decent" pictures of the couple from the same spot a few days earlier.
Valerie Suau, who works for La Provence regional newspaper, said she was astonished that the residence where they were holidaying had not been heavily guarded. She said she was "given free rein" to do what she liked without being stopped.
Yesterday, a royal aide said that the couple hoped a criminal investigation would also be launched by the French police, which they would be happy to support.
Under French law, breach of privacy is a criminal offence carrying a maximum fine of about €45,000 and a possible one-year jail sentence for the editor of Closer and for the photographer.