James Murdoch has denied "storming" into the Independent's newsroom to confront its editor over a poster campaign featuring his father.
But the media mogul admitted using "colourful language" when he confronted the newspaper's former editor-in-chief Simon Kelner over what he saw as a personal attack on his father.
The Leveson Inquiry heard that the campaign in 2010 featured billboards that read: "Rupert Murdoch won't decide this election - you will."
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James Murdoch told the inquiry he had been visiting Associated Newspapers - based in the same building as the Independent - and decided to visit Kelner to voice his concerns over the campaign.
"I was upset and concerned because the Independent had not run an article about this but had put up a load of giant billboards around England that I had seen pictures of, with the message 'Rupert Murdoch won't decide this election'.
"I thought they were really personalising an agenda against my father and my family that I found inappropriate."
He said he found himself in the middle of the newsroom, due to a lack of a reception or front desk, but had not intended to.
He said he asked Kelner to speak to him and they went into an office, where he raised his concerns, adding:
"Whether or not I used colourful language I wouldn't dispute."
But he denied there was any "storming".
He said: "I was certainly upset because Kelner had been availing himself of the hospitality of my family for years and
I thought it was beyond the pale and not a decent way to go about his business."
Tweeting after the evidence, Kelner rejected Murdoch's claims, saying:
Earlier James Murdoch admitted to meeting David Cameron 12 times while the Tory leader was in opposition.
He also told the inquiry the News of the World should not have run the Max Mosley "Sick Nazi Orgy" story, which led to the former Formula 1 boss receiving more than £60,000 in compensation.
Labour MP Tom Watson, one of News International's chief critics in Parliament, has described James Murdoch's evidence as "fascinating".