The Prime Minister insisted he had been clear about his present and future plans on tax, which included a promise never to benefit from money held offshore.
But in a bombshell admission he told ITV News: "I should deal with the past as well. Because of course I did own stocks and shares in the past - quite naturally because my father was a stockbroker.
"I sold them all in 2010, because if I was going to become Prime Minister I didn't want anyone to say you have other agendas, vested interests.
"Samantha and I had a joint account. We owned 5000 units in Blairmore Investment Trust, which we sold in January 2010. That was worth something like £30,000 (NZ$62,296)."
Mr Cameron said he paid income tax on the dividends but did not have to pay capital gains tax because the profit was too low.
He said: "But it was subject to all the UK taxes in all the normal way. So I want to be as clear as I can about the past, present and future.
"Because frankly I don't have anything to hide. I am proud of my dad and what he did, the business he established and all the rest of it. I can't bear to see his name being dragged through the mud.
"For my own, I chose to take a different path from my father, grandfather and great grandfather, who were all stockbrokers, and I have nothing to hide in my arrangements."
In the interview, the PM said he did believe proper payment of tax was a "moral" issue.
Mr Cameron said the claims about his father had made this week a "difficult few days".
He said: "I think a lot of the criticisms are based on a fundamental misconception, which is that Blairmore Investment, a unit trust, was set up with the idea of avoiding tax. It wasn't. It was set up after exchange controls went so that people who wanted to invest in dollar denominated shares and companies could do so.
"And there are thousands of other unit trusts set up in this way. It was reported to the HMRC, the Inland Revenue, it reported itself every year. It was properly audited."
The Prime Minister insisted he could not certain where the £300,000 (NZ$623,106) inherited from his father had been made.
But he acknowledged: "But in all of this I've never hidden the fact that I am a very lucky person. I had wealthy parents who gave me a great upbringing.
"Who paid for me to go to an amazing school. I have never tried to pretend to be anything I am not. And I am lucky, in that I earn a good salary as prime minister, my wife is successful and earns money and we own two very nice houses.
"So I am not pretending anything. But I was keen in 2010 to sell everything, shares, all the rest of it, so I can be very transparent. I don't own any part of any company, any investment trust, anything like that."
Mr Cameron added: "He left me some money, very generously, quite a lot of money. It was £300,000 (NZ$62,296).
"I obviously can't point to every source of every bit of the money, and dad isn't around to ask the questions now.
"He was a very hardworking man who built up a business. He left his house to my brother. He left me some money. And left things to my brothers and sisters too. And I think there is transparency about all of that.
"And in the future I am not benefiting from any Cameron family trusts. At the moment I own no shares, no investments. I have savings."
Mr Cameron said he would be happy to publish his tax return - and those for recent years - despite the fact he will not run for a third term as Prime Minister.
He said: "I am very happy to get on and do that now. Whether we get on and do it every year, or starting now, or going back a couple of years, I am very happy with that.
"And that will be a big change. So we shouldn't dive into it and insist everyone does it.
"But if people want the prime minister and potential prime minister, as I said before I am relaxed about that, I am happy to do that."
All MPs should not have to take the same step, Mr Cameron said.
In a bid to close down a toxic row over tax avoidance earlier this week, Mr Cameron made an extraordinary public statement about his personal finances and income - insisting he received no money from shares or offshore trusts.
But the statement only suggested more questions and Downing Street was forced to issue a string of further clarifications - making a total of four statements.
Ian Cameron was named in the massive leak of more than 11 million files from the Panama tax haven.
Shortly before his death the former stockbroker personally owned more than 6,000 shares in a Jersey fund he helped to manage, known by various names including the Close International Equity Growth Fund.
The assets in Jersey were left to the Prime Minister's mother Mary in 2010, leaving open the possibility that Mr Cameron could eventually benefit from it in the form of an inheritance.
The leaked papers revealed Ian Cameron's firm Blairmore Holdings avoided UK tax for years by operating out of the Bahamas and Jersey.
Under Jersey law, the value of the assets does not have to be made public, but a grant of probate is normally required only for sums above £10,000 (NZ$20,767). It cannot include property but can apply to cash held in bank accounts or investments, including offshore trusts and funds, known as 'movable estate'.
According to his English will, Ian Cameron left everything to his widow Mary, apart from specific bequests to the Prime Minister and his sisters. Legal sources said the terms of the will meant any Jersey assets were most likely to have gone to Mrs Cameron.
Downing Street's latest statement said the Prime Minister and his family will not benefit in the future from any offshore funds. But tax experts said funds held in Jersey would have grown more quickly, as dividend payments would not have been subject to tax.
If Mr Cameron inherits anything from his mother it could then be argued that he has benefited from the offshore Jersey assets.
Chartered accountant and tax lecturer Robert Leach said: "It's quite possible that Mr Cameron and his siblings could benefit from money held offshore if they inherit any of Mary Cameron's estate.
Mr Cameron insisted he had a good record on tackling tax avoidance as PM. Photo / AP
"If this happens it will be difficult to reconcile this with the Prime Minister's statement."
There are legitimate reasons to hold money and other assets offshore and there is no suggestion of illegality or wrongdoing by any member of the Cameron family.
Documents filed in 2009 showed Ian Cameron held at least 6,000 shares in the Jersey fund - the first time he was shown to have personally held wealth offshore rather than managing funds like Blairmore Holdings in Panama.
After his death, the net value of his estate was put at £2.7million (NZ$5.6 million). He left £300,000 (NZ$623,106) in cash - just under the threshold at which inheritance tax is paid - to David.
A £1million (NZ$2 million) mews house in Kensington, West London, was left to the Prime Minister's sisters Tania and Clare. The remainder of his estate was left to Mrs Cameron. The £2.5million (NZ$5.2 million) family home near Newbury in Berkshire was transferred to the Prime Minister's older brother Alex in 2006, in an apparent attempt to reduce inheritance tax liabilities.
Labour has repeatedly called for Downing Street to publish the full details of Mr Cameron's links to Blairmore. Mr Leach said that the Prime Minister needed to say if the £300,000 (NZ$623,106) he received from his father's will "was the proceeds of a scheme that avoided tax".
He added: "The answer is probably yes as he would have denied it otherwise. But even then he has not done anything illegal, although it is politically embarrassing."
