In a radio interview Jose Mujica offered “heartfelt apologies” and blamed the quip on his “rough language skills”.
Last week, Jose Mujica was overheard saying: “This old hag is even worse than the cross-eyed man.”
It was claimed that the Uruguayan president referred to Cristina Fernandez de Kirchner and her late husband, whom she succeeded as president.
Cristina Fernandez’s husband, Nestor Kirchner, had a lazy eye. He died suddenly of a heart attack in 2010.
The comments, meant to be private, were accidentally caught and recorded by a nearby open microphone.
Jose Mujica’s words caused outrage in Argentina and led to an official protest.
In an interview to radio M24 on Thursday, Jose Mujica put the comments down to his “rough” past life in an armed group.
“We can’t avoid that our daily and intimate manner of speaking is sometimes rough,” the president said, adding that it has been shaped by spending many years in prison cells and detention.
“This kind of language is miles away from public speeches, from the press. It has only to do with intimate relationships between very few.”
Jose Mujica made the controversial comments at the start of a news conference while speaking quietly to another official.
El Observador newspaper posted the audio on its website, claiming that the president did not realize that the microphones were on.
The newspaper said that its website had crashed because of historically high levels of traffic generated by its coverage of the incident. It also gained the attention of social media.
Argentine Foreign Minister Hector Timerman summoned the Uruguayan ambassador in Buenos Aires, Guillermo Pomi, to protest about the comments.
Correspondents say that President Jose Mujica, 77, who took office in 2010, has clashed in the past both with Cristina Fernandez and Nestor Kirchner.
Relations between Uruguay and Argentina have recently been strained because of concern in Montevideo over what it sees as protectionist measures enforced by Buenos Aires.
Nestor Kirchner was Argentina’s president from 2003 to 2007. His wife, Cristina Fernandez de Kirchner succeeded him and won re-election in 2011.
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