The publication of crime scene photographs of Michaela McAreavey, who was murdered on her honeymoon in Mauritius, marks a new low, her family said.
The Sunday Times in Mauritius, which has no connection to any British or Irish newspaper, used police images of the hotel room where she was killed.
The Taoiseach Enda Kenny and Stormont Deputy First Minister Martin McGuinness have also condemned the publication. Michaela and John McAreavey were staying at the Legends Hotel on the island in January last year. Last week, two men were acquitted of her murder after an eight-week trial.
A statement from the couple's families said: "As the families struggle to come to terms with the result from the trial, this action by the newspaper is not only insensitive to their grief but marks another low in the treatment of John, the two families and the dignity of Michaela."
Twelve black and white images of the crime scene were published in the newspaper yesterday.
On the front page there is a photograph of Ms McAreavey taken after her death – under the headline "Exclusive". Inside there are more images of the crime scene, including the hotel room and the bathroom.
Mr Kenny said: "The publication of these images represents an appalling invasion of privacy and is a gross affront to human dignity."
Mr Gilmore said the decision to publish the images was unacceptable and showed a complete lack of respect to the McAreavey and Harte families.
The Tanaiste, who confirmed he had spoken to Mr McAreavey since his return from Mauritius but would not say what they talked about, said it appeared the photographs had been leaked by authorities.
Mr Gilmore also refused to rule out the possibility of sending Irish detectives to undertake their own investigation into the murder - like French authorities did following the murder of Sophie Toscan du Plantier in Co Cork in 1996.
"That is something we may have to look at down the line," he added.
"But the immediate issue that arises today arises firstly from the publication of the photographs. We have to take immediate action to deal with that."
Yesterday, Taoiseach Enda Kenny and Stormont deputy first minister Martin McGuinness also condemned the newspaper, which has no connection to any British or Irish company.
Mr McAreavey and other family members returned home from Mauritius at the weekend, after a gruelling eight-week trial.
Legends hotel workers Sandip Moneea and Avinash Treebhoowoon were cleared of Mrs McAreavey's killing by a jury at the Supreme Court in Port Louis last Thursday.
Mrs McAreavey, 27, was the daughter of Tyrone gaelic football manager Mickey Harte.
The teacher was found dead in the bathtub of her deluxe room shortly after lunching with her husband at a poolside restaurant.
Both defendants worked at the hotel at the time.
Elsewhere the Mauritius Police Force confirmed an investigation into the publication of the photographs has been launched.
"A police investigation is under way, the CID is investigating the matter," said a spokeswoman.
"So far we have not received the report yet.
"We shall have to wait for the outcome in that respect."
Meanwhile, a travel agent in Co Donegal has stopped selling trips to Mauritius out of solidarity to Mrs McAreavey's family.
Caroline Davies, who owns Liberty Travel in Letterkenny, said she was disgusted after details emerged during the trial of how authorities treated Mr McAreavey in the aftermath of his wife's death.
"They locked him in a room and told him he would find another wife. I thought that was appalling," said Ms Davies.
"So I took the decision not to sell Mauritius as a mark of solidarity to the family."
The travel shop owner said Mauritius was not a big seller anyway, however it has divided opinion among holidaymakers.
"I've had some people come in since the murder saying 'I hope you're not selling Mauritius', but then others have told me what happened wouldn't put them off going," she said.
Ms Davies added that she would not sell a holiday if it is not somewhere she would be willing to travel to herself.