Mr Murdoch said Mr Brown called him after the Sun switched its allegiance to the Conservative Party in September 2009.
The newspaper's former editor Kelvin MacKenzie previously said Mr Brown "roared" at the 81-year-old for 20 minutes and declared war on him.
Mr Murdoch today told the inquiry that Mr MacKenzie's account was a "colourful exaggeration", playing down the conversation, but went on to say that Mr Brown was not in a balanced state of mind.
"Mr Brown did call me and said, 'Rupert, do you know what's going on here?', and I said, 'What do you mean?'.
"He said, 'Well the Sun and what it's doing and how it came out'.
"And I said, 'I am not aware of ... I was not warned of the exact timing, I'm not aware of what they are saying, I am a long, long way away. But I am sorry to tell you Gordon, we have come to the conclusion that we will support a change of government when and if there is an election. Not if, but when there is an election'.
"And he said - and I must stress no voices were raised, we were talking more quietly than you and I are now - he said, 'Well, your company has declared war on my government and we have no alternative but to make war on your company'.
"And I said, 'I'm sorry about that Gordon, thank you for calling', and end of subject."
Asked by counsel for the inquiry how Mr Brown might have "made war" on his company, Mr Murdoch said he did not know, but added: "I did not think he was in a very balanced state of mind."
Mr Murdoch told the inquiry at the Royal Courts of Justice that Mr Brown made a "totally outrageous" statement after the phone hacking scandal broke, suggesting the story in 2006 about his son Fraser having cystic fibrosis had been obtained illegally.
The media mogul, whose wife Wendi Deng and son Lachlan were in court, said: "He later, when the hacking scandal broke, made a totally outrageous statement which he had to know was wrong, when he called us a criminal organisation.
"Because he said that we had hacked into his personal medical records, when he knew very well how The Sun had found out about his son, the condition of his son, which was very sad."
He said the newspaper had been contacted by a father in the same position as Mr Brown, giving them the information.
"Mrs Brooks [former editor Rebekah Brooks] immediately snatched it from the newslist and said, 'let me handle this'.
"She called Mrs Brown and said, 'look this is going to be out, we should be careful, how would you like it handled?"'
Mr Murdoch said the story was published a few days later, and added: "Mr Brown wrote a personal letter to Mrs Brooks thanking her for her sensitivity and the way she handled the story.
"I believe that letter is in the hands of the police."
In his statement, Mr Murdoch said he had been impressed by Tony Blair for a long time and today regards him as a personal friend.
The inquiry heard the then-Labour leader travelled to Hayman Island in Australia to address the annual News Corporation conference in July 1995.
Mr Murdoch admitted he may have made the comment, reported by Mr Blair: "If our flirtation is ever consummated, Tony, then I suspect we will end up making love like porcupines, very very carefully."
But Mr Murdoch denied his relationship had ever led to any favours from the prime minister.
"You are making sinister inferences," he told Mr Jay.
"I want to say that I, in 10 years of his power, never asked Mr Blair for anything.
"Nor indeed did I receive any favours. If you want to check that, I think you should call him."
He told the inquiry he saw Mr Blair two or three times a year.
"It's not as though there was a constant approach or daily text messages as happened with some newspapers," he said. "We had no such relationship."
The inquiry heard that all of Mr Murdoch's newspapers backed the Gulf War in March 2003, and that there were three phone calls between Mr Blair and Mr Murdoch that month.
Mr Murdoch defended the right of newspapers to investigate people in public positions, including MPs, celebrities and even newspaper proprietors.
He gave the example of The Sun's recent publication of revelations from a new biography of music mogul Simon Cowell.
"I don't believe in using hacking, I don't believe in using private detectives or whatever," he said.
"I think that is just a lazy way of reporters not doing their job. But I think it is fair when people are held up as great, or have themselves held up as iconic figures or great actors, that they be looked at.
"We've just seen an example of it with Mr Simon Cowell. He wanted to have it all himself."
Mr Murdoch praised the Daily Telegraph's exposure of MPs' abuses of the parliamentary expenses system.
He said: "I really welcomed - I was jealous of - the Daily Telegraph buying all the personal expense accounts of the Members of Parliament...
"I thought that was a great public service. I have to say that I am disappointed the editor of The Times didn't buy them when they were offered to him first."
The billionaire told Robert Jay QC, counsel to the inquiry, there was nothing sinister about his contacts with prime ministers.
"I go to an election every day, Mr Jay. People can stop buying my newspapers any time - often do, I'm afraid," he said.
"And it's only natural for politicians to reach out to editors, and sometimes proprietors if they are available, to explain what they are doing and hoping it makes an impression and it gets through. But I was only one of several."
He added: "If any politician wanted my opinions on major matters, they only had to read the editorials in The Sun."
Mr Murdoch told the inquiry he wanted to "put some myths to bed".
The 81-year-old said rumours that he had not forgiven Prime Minister David Cameron for setting up the inquiry were untrue.
Giving evidence, he said he welcomed the probe: "I think the need is fairly obvious, there have been some abuses shown. I would say there have been many other abuses but we can all go into that in time.
"The state of the media in this country is of absolutely vital interest to all its citizens.
"Frankly, I welcome the opportunity because I wanted to put some myths to bed."
He was asked about his relationships with several prime ministers, including Baroness Thatcher, whom The Sun supported in the election of 1979.
Mr Murdoch, News Corp's chairman and chief executive, met her for lunch at Chequers on January 4 1981 during which he discussed his plans to buy The Times and The Sunday Times.
But again he said he did not ask her for any favours and she did not offer him any.
Mr Murdoch rejected suggestions that he was a "Sun King" figure who used his charisma to exert his authority over his worldwide media empire.
He also denied claims that he used his titles to promote his business interests.
He said: "I take a particularly strong pride in the fact that we have never pushed our commercial interests in our newspapers."
He said he never gave instructions to editors.
"Sometimes when I was available on a Saturday I would call and say 'What's the news today?' It was idle curiosity perhaps.
"Other times I would ring on a Tuesday from New York when the Sunday Times came in, and I would say 'That was a damn fine newspaper you had this week'. I perhaps wouldn't have read the editorial."
The mogul admitted being closer to The Sun than the News of the World, saying: "It was a daily paper, there was always something more urgent about it."
Asked about the publication of Hitler's supposed diaries - later found to be fakes - by the Sunday Times in 1983, he said: "It was a massive mistake I made and I will have to live with for the rest of my life."
Mr Murdoch admitted giving former Sun editor Kelvin MacKenzie a "bollocking" after the headline "It's The Sun Wot Won It" appeared on the front page of the newspaper in April 1992 after the Conservatives' general election victory.
He said: "I thought it was tasteless and wrong for us. It was wrong in fact - we don't have that sort of power."
He went on to say of The Sun: "I think we are perhaps the only independent newspaper in the business."
Mr Murdoch denied only backing "winning candidates", saying: "I try to judge the candidate on the issues.
"I never let my commercial interests, whatever they are, enter into any consideration of elections."
Mr Brown later said that Mr Murdoch's claim about him "declaring war" on
News Corporation was "wholly wrong" and called on the media mogul to correct his account.
In a statement, the former prime minister said: "Mr Rupert Murdoch has today made a serious allegation that, in a telephone call when The Sun declared for the Conservative Party, I told him I had declared war on his company.
"He is wholly wrong.
"As the Leveson Inquiry
heard, The Sun declared for the Conservatives on the 30th of September 2009. I did not phone Mr Murdoch or meet him, or write to him about his decision.
"The only phone call I had with Mr Murdoch in the last year of my
time in office was a phone call specifically about Afghanistan and his newspaper's coverage of the war. This was in the second week of November
after his newspaper, The Sun, printed a story in the second week of November about the death of a soldier and his mother's complaints .
"I hope Mr Murdoch will have the good grace to correct his account."
PA
