Cameron's initial reluctance to admit that he had benefited from the fund caused a furore, compounding his problems when he faces a huge political fight to persuade Britons to vote to stay in the European Union in a June 23 referendum.
The EU issue has split his Conservative Party, while the government has also been going through a tough patch over a senior minister's resignation, a u-turn on welfare cuts and accusations it is failing to protect Britain's steel industry.
After saying on Saturday that he could have handled the fallout from the Panama disclosures better, Cameron released a summary of his tax records for the past six years.
But any hope that this would draw a line under the row was short-lived, as the main Sunday newspapers zeroed in on a gift of 200,000 pounds Cameron received from his mother in 2011, suggesting it may be a way of avoiding inheritance tax.
A source at Cameron's Downing Street office said the suggestion was inaccurate, the gift had been declared and this was about a mother making a gift to her son in the same legal way that hundreds of thousands of Britons do every year.
Cameron will make a statement about tax policy to parliament on Monday, but is likely to face a barrage of questions about his personal finances from Labour MPs.
Labour Party leader Jeremy Corbyn has accused him of misleading the public by issuing what Corbyn described as four "weasel-worded" statements in as many days before finally admitting that he had benefited from his father's fund.
Some politicians who are campaigning for Britain to vote to stay in the EU in June's referendum are concerned that the damage to Cameron is bad for their side, as he has previously been considered the best advocate for an "In" vote.
"The scandals over David Cameron's finances ... may tip the decision further towards 'Leave'," said former Scottish National Party leader Gordon Wilson in a statement on Sunday.
Cameron is not accused of having done anything illegal, and the fact that he is a wealthy man is nothing new.
But the past week has been damaging because the drip-drip of carefully worded statements before the fuller disclosure created the impression he may have had something to hide.
"He's not behaved improperly in any way and he's gone further than any prime minister previously in publishing these tax returns," Conservative minister Dominic Raab told Sky News television, accusing Cameron's Labour critics of "unsavoury" personal attacks and comparing them to "hyenas".
Bookmakers William Hill said they had cut their odds on Cameron resigning as prime minister this year to 2/1 compared with 16/1 when he won the last general election last May.
Cameron said on Thursday his father's investment trust was not set up to avoid tax but to invest in dollar-denominated shares. He said he had paid all taxes due on his own investment, which was worth about 30,000 pounds when he sold it in 2010.
However, Cameron stands accused of hypocrisy after portraying his government as being in the forefront of global efforts to crack down on offshore tax havens. A comment he made in 2012 about a famous comedian's legal tax avoidance scheme being "morally wrong" has been widely quoted by media.
Scores of politicians and business figures have been implicated in the Panama Papers, including the prime minister of Iceland who has since stepped down. The 11.5 million documents leaked from the Panamanian law firm Mossack Fonseca detail the creation of more than 200,000 companies in offshore tax havens.
The documents disclosed by Downing Street on Sunday, from RNS Chartered Accountants, show Cameron paid tax of 75,898 pounds on income of 200,307 pounds in the 2014-2015 financial year, the most recent one included.Seeking to regain the initiative, Cameron announced a new taskforce, jointly led by Britain's tax authority and National Crime Agency, to tackle money laundering and tax evasion.
But Labour's Shadow Chancellor, John McDonnell, said this was inadequate and called for a full public inquiry.