The Mail printed 25,000 special copies of its Sunday edition made up to look like the Tribune.
"I am appalled and shocked that another newspaper would stoop so low to plagiarise a front page lookalike of the Sunday Tribune with the naked ambition of gaining extra circulation.
"The Mail On Sunday has shown in this act that it will leave no stone unturned in the race to the bottom.
"The Tribune management and staff and indeed Jim Luby the Receiver are working flat out in the hope of keeping the newspaper afloat. We are talking about 43 jobs in Ireland here, not extra remuneration for Associated Newspapers back in the UK."
Sebastian Hamilton, the newspaper's editor, reportedly defended the move, claiming that the Mail "wanted to make sure those readers were aware that the Irish Mail on Sunday is an Irish paper."The Irish secretary of the NUJ, Séamus Dooley, described the move as "crass and cynical".
"This was an attempt to confuse readers and to cash in on the crisis at the Sunday Tribune in a crass manner which does no credit to the Irish Mail on Sunday or publishers, Associated Newspapers," he said.
Ireland's trading standards body, the National Consumer Agency, says it is considering action against Associated Newspapers, after the Sunday Tribune and the NUJ both lodged formal complaints.
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