The Prime Minister has faced intense pressure to detail his interests since the Panama Papers leaks included details of Blairmore Holdings - which used "bearer shares" to protect investors' privacy.
In an interview with ITV News, he insisted it was a "fundamental misconception" that it was set up to avoid tax, saying his father Ian was being "unfairly written about".
And he said that while his and Samantha's profit from the scheme was "subject to all the UK taxes in the normal ways" - it came to just below the threshold at which capital gains tax would have applied.
Number 10 said Mr and Mrs Cameron bought their holding in April 1997 for £12,497 and sold it in January 2010 for £31,500.
The annual personal allowance for an individual in 2009-10 was £10,100 - meaning jointly the profit was just outside the threshold.
Mr Cameron, who has been a prominent campaigner for increased tax transparency, also repeated his willingness to publish his own tax returns.
Downing Street later confirmed this will take place "as soon as possible".
When questions first emerged this week about the PM's tax affairs, Downing Street initially said it was a private matter before first clarifying Mr Cameron had no offshore funds and trusts and then making clear the family would not benefit in the future either.
Opposition MPs used the latest admission from Mr Cameron to criticise his reputation and handling of the issue, with Labour's John Mann suggesting the PM "has no choice but to resign".
Labour deputy Tom Watson suggested Mr Cameron should consider "voluntarily paying the money that, in his own words, should morally belong to the exchequer".
He also said the PM may have to resign although added it is "too early to tell".
Speaking to ITV, Mr Cameron said: "I paid income tax on the dividends, but 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 ways.
"So 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.
"I'm proud of my dad and what he did and the business he established and all the rest of it.
"I can't bear to see his name being dragged through the mud, as you can see, and for my own, I chose to take a different path from my father, grandfather and great-grandfather, who were all stockbrokers, and I've got nothing to hide in my arrangements and I'm very happy to answer questions about it."
Mr Cameron said it had been "a difficult few days" since the mass leak of records from Panamanian law firm Mossack Fonseca as he launched a staunch defence of his father.
He also said he was not able to "point to every source of every bit of the money" that his father left him when he died - which he said amounted to around £300,000.
Pressed on whether he benefited from any part of the estate that was based in Jersey, he said: " Dad's not around for me to ask the questions now. But he was a very hardworking man. He 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, you know, there's pretty good transparency about all of that. And as I've said, in the future I'm not benefiting from any Cameron family trust. At the moment I own no shares, no investments. I have savings."
For Labour, Mr Watson told Sky News: " He may have to resign over this but I think we need to know a lot more about what his financial arrangements have been, why it's taken three days for him to answer legitimate questions from journalists, why he didn't come clean when he heralded in the new age of transparency, and what other shareholdings does David Cameron have or has had since he was a Member of Parliament."
SNP economy spokesman Stewart Hosie said Mr Cameron has "played the public" over the issue, adding he must "come clean" on other tax-related issues.
He said: "The public will understandably now find it hard to trust the Prime Minister."
Mr Watson also accused the Prime Minister of hypocrisy.
Speaking to the BBC, he said Mr Cameron could not be blamed for his father's actions but added: "He can for hypocrisy. He said that sunlight is the best disinfectant and wasn't entirely straight with the British people about what his own financial arrangements were.
"That wouldn't be so bad if he hadn't also been lecturing very prominent people about their own tax arrangements, some he called morally wrong for being invested in similar schemes.
"People don't like that and they want a lot more answers from David Cameron before this scandal goes away."
Skills Minister Nick Boles suggested Mr Cameron regrets the way the disclosure about his tax affairs had been handled.
He told the BBC Radio 4 Today programme: "I'm sure that, with the benefit of hindsight, he would rather that all of what has come out over the last four days had come out on the first day.
"I think the instinct is one that we all can identify with, even if it was something that he might well have done differently if given a second chance."
He added: "I think he thought 'I know that I have complied fully with all of the tax laws' and I don't like feeding this mill of preying on his father's memory and his father cannot defend himself."
Shadow work and pensions secretary Owen Smith said Mr Cameron needed to be "clear" about all his past investments and should "allow sunlight to disinfect him".
He told Today: "The Prime Minister now needs to come to the country - I think he should do it in Parliament next - and come clean about what the Government's real intentions are about tax avoidance."
He added: "People will now have doubts about the trustworthiness of the Prime Minister, given that he has been so revealed as having double standards, speaking out of both sides of his mouth, not being true to what he said he would do when he came to power."