The PM has faced questions over Blairmore Holdings, an offshore company set up by his late father, Ian, the BBC wrote.
He told ITV News he had paid all UK taxes due on the profits he made from the sale of the shares and said the firm had not been set up to avoid tax.
Labour said the PM had been forced into the "extraordinary admission".
The BBC understands Mr Cameron will publish his tax returns, possibly next week.
There have been days of headlines about Blairmore Holdings, a fund for investors which, until 2006, used "bearer shares" to protect its clients' privacy, following the leak of 11 million documents held by Panama-based law firm Mossack Fonseca.
They show that Ian Cameron, who died in 2010, was one of five UK directors who flew to board meetings in the Bahamas or Switzerland.
Read alsoPanama govt announces creation of 'panel of experts'On Wednesday, Downing Street issued a statement saying Mr Cameron, his wife and children did not benefit from offshore funds - following a day of questions from the media about whether his family retained an interest in the fund.
On Thursday Mr Cameron told ITV News: "I don't have anything to hide. I'm proud of my dad and what he did and the business he established... I can't bear to see his name being dragged through the mud."
The PM said it had been a "difficult few days, reading criticisms of my father and his business practices - my dad, a man I love and admire and miss every day".
Mr Cameron said much criticism was based on a "fundamental misconception" that Blairmore Investment was set up to avoid 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 many other, thousands of other unit trusts set up in this way," he said.
Mr Cameron said the fund was "properly audited" and reported to the Inland Revenue every year. Anyone who bought units in it was subject to capital gains tax when shares were sold, he said.
He said that he had owned stocks and shares in the past but sold them in 2010 shortly before he became prime minister.
"I didn't want to anyone to say you've got other agendas or vested interests," he said.
"Samantha and I had a joint account and we owned 5,000 units in Blairmore investment trust which we sold in January 2010, that was worth something like GBP 30,000.
"I paid income tax on the dividends, but there was a profit on it, but that 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 ways."
Downing Street said Mr and Mrs Cameron bought their holding in April 1997 for GBP 12,497 and sold it in January 2010 for GBP 31,500. That year the personal allowance before capital gains tax was paid was GBP 10,100 per person.
