Mr Barenboim, who is Jewish, was approached by the reporter, Dafna Arad, on Thursday during the launch of a book he wrote with the late Edward Said, a leading Palestinian intellectual.
Ms Arad wore her military uniform, as is the custom for Army Radio reporters still serving their mandatory military service. She said in a report on Army Radio: "I wanted to ask Mr Barenboim about the concert he conducted in Ramallah last week, about his musical vision and more. But he wouldn't agree to talk to me and started signing the book. I insisted. Then he said he refused to be interviewed by a soldier in a uniform and that he will agree to talk to me only if I come to him in civilian clothes."
When she protested that she had no choice but to wear the uniform, Mr Barenboim pulled on her epaulettes and yelled at her, she said.
The education minister, Limor Livnat, was outraged by the incident and said the conductor was "a real Jew-hater, a real anti-Semite."
Mr Barenboim, who was born in Argentina and raised in Israel, has had frequent spats with Israel's government. Last year, he angered Israeli officials when he criticised the occupation of the West Bank and Gaza.
The conductor, in a telephone interview with Army Radio yesterday, did not deny the incident and defended his actions.
"Anti-Semitic? What is anti-Semitic about it? When I say a uniform should be worn to the right places and not to the wrong ones, there is nothing anti-Semitic about it, there is no logic to this," Mr Barenboim said. "I just thought that in this place, discussing a book written together with a Palestinian, it shows lack of sensitivity."
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