Cameron said he would publish his tax returns and shouldered the blame for the row over his financial affairs.
‘It has not been a great week. I know that I should have handled this better, I could have handled this better,’ he told his Conservative Party's spring forum in London.
‘I know there are lessons to learn and I will learn them.
‘Don't blame Number 10 Downing Street or nameless advisers, blame me.’
Cameron and his Downing Street office issued four comments regarding the Panama Papers before the premier on Thursday finally admitted he had held shares in his late father's Bahamas-based offshore investment fund.
Cameron admitted he had held a stake in the fund and sold it for around £30,000 (37,000 euros, $42,000), four months before he became prime minister in 2010.
The revelations in the Panama Papers, resulting from what the Panamanian law firm Mossack Fonseca blamed on a computer hack launched from abroad, revealed how the world's wealthy stashed assets in offshore companies.
Demonstrators were set to gather outside Downing Street later Saturday to call for his resignation.
‘The facts are these: I bought shares in a unit trust -- shares that are like any other sorts of shares and I paid taxes on them in exactly the same way,’ Cameron said.
‘I sold those shares. In fact, I sold all the shares that I owned, on becoming prime minister.
‘And later on I will be publishing the information that goes into my tax return, not just for this year but the years gone past because I want to be completely open and transparent about these things.
‘I will be the first prime minister, the first leader of a major political party, to do that and I think it is the right thing to do.’