Mr Menem was forced to make his remarks after the Sun published an article in his name that claimed he had made an "historic apology" for the conflict 16 years ago.
Writing ahead of his visit to London next week, the Argentinian president declared in the article that "the conflict should never have happened, we deeply regret it".
Mr Menem, who will lay a wreath at the Falklands war memorial in St Paul's Cathedral, said the conflict that claimed more than 1,000 British and Argentinian lives had been a "sad and traumatic blot in the history of our relations".
The paper's front-page headline said: "Argentina Says: We're Sorry for Falklands", and ministers and the Opposition welcomed the "apology".
However, within hours Mr Menem was busy denying the account of his words to reporters in Buenos Aires. "Saying sorry is completely different. That is not the way I expressed it," he said.
Turning what was a carefully-worked media operation into a diplomatic embarrassment, he also made clear that Argentina was not giving up its claim to the Malvinas and demanded the release of the former Chilean dictator, General Augusto Pinochet.
It emerged yesterday that government spin doctors had helped in the drafting of the article, with Tony Blair's press secretary, Alastair Campbell, playing a key role in the process. Mr Campbell was believed to have written a similar Sun article earlier this year in which the then Japanese Prime Minister, Ryutari Hashimoto, expressed "deep feelings of remorse and heartfelt apology" for Japan's treatment of British PoWs in the Second World War.
A Downing Street spokesman admitted Mr Campbell had been involved in the contacts between Mr Menem's office and the Sun. "Following the success of the Hashimoto article, the editor of the Sun asked the Prime Minister's press secretary to approach the Argentine government for an article from President Menem. The president was happy to do this as a way of building on the theme of reconciliation of next week's visit."
The spokesman said that the Government welcomed the Sun article as a "powerful gesture of reconciliation", but denied that Number 10 had directly written the piece.
"The words are the words of the Argentinians. We would provide advice on style as you would expect, but the contents were entirely theirs," he said.
The spokesman for Downing Street also denied that the Sun's headline had been cleared by Number 10, but the paper's editor, David Yelland, made it clear that Mr Campbell had known how the article would be presented. "Everybody involved in this very complicated negotiation to get this thing in the paper knew that the headline would be 'sorry'," he said.
Sir Rex Hunt, governor of the Falklands during the war, welcomed the expression of regret, but said Mr Menem should make a "genuine apology" for the invasion.Reuse content