Video report by ITV News Political Editor Robert Peston
David Cameron and his wife owned shares in the Panamanian trust set up by his late father, before selling them for around £30,000 in 2010, he has exclusively told ITV News.
Mr Cameron said he made a profit on around 5,000 units the couple owned in Blairmore Investment Trust, but insisted the money was subjected to UK tax rules.
He also divulged details of his £300,000 inheritance and said recent criticism of his father was "unfair".
The Conservative leader was dragged into the the Panama Papers scandal after leaked documents from law firm Mossack Fonseca included details of a multi-million-pound offshore firm set up by his father.
Downing Street has been forced to issue four statements on the matter, initially saying it was a "private matter" whether the Cameron family still had funds in offshore investments, before stating they "do not benefit from any offshore funds" and there are none they will benefit from in the future.
Today the prime minister told ITV News: "We owned 5,000 units in Blairmore Investment Trust, which we sold in January 2010. That was worth something like £30,000.
"I paid income tax on the dividends. There was a profit on it but it was less than the capital gains tax allowance so I didn't pay capital gains tax. But it was subject to all the UK taxes in all the normal way.
"I want to be as clear as I can about the past, about the present, about the future, because frankly I don't have anything to hide."
Since the scandal was exposed there has been criticism of the arrangements under Blairmore, including of Mr Cameron's father, and suggestions the prime minister only reached his position because of his privileged upbringing.
Mr Cameron said he received a £300,000 inheritance from his father when he died.
"I obviously can't point to every source of every bit of the money and dad's not around for me to ask the questions now," he said.
"In all of this I've never hidden the fact that I'm a very lucky person who 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.
"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 or any investment trust or anything else like that."
The prime minister admitted it had been "a difficult few days" hearing criticism of his father and said much of it was based on a "misconception" that Blairmore was set up to avoid tax.
"It wasn't," he said. "It was set up after exchange controls went so that people who wanted to invest in dollar denominated shares and companies could do so."
Mr Cameron added: "There are many other unit trusts like it, and I think it's being unfairly described and my father's name is being unfairly written about."
Labour leader Jeremy Corbyn has said it is in the prime minister's "own interests" to disclose details of his family's arrangements with offshore tax havens.
Mr Corbyn said he wanted an investigation conducted by Revenue and Customs "about the amount of money of all people that have invested in these shell companies or put money into tax havens and to calculate what tax they should have paid over the years".
Labour MP Jess Phillips branded Ian Cameron's tax arrangements "utterly disgusting".