David Cameron faced calls to be "straight" with voters about all his private financial affairs after disclosing that he had benefited from an offshore fund set up by his late father.
The Prime Minister sold his and wife Samantha's shares in Blairmore Holdings - one of the tax haven schemes exposed in the Panama Papers leaks - in 2010 and insisted it was not set up as a tax dodge.
But opposition politicians said he had given the clear impression he had something to hide by only revealing his involvement after days of pressure and a string of statements that failed to mention past investments.
They are pushing for the PM to come to the Commons on Monday to answer questions about the leak of millions of documents from Panama law firm Mossack Fonseca, which have linked many senior politicians to offshore schemes.
Mr Cameron said it was a "fundamental misconception" that Blairmore was set up to avoid paying UK tax and stressed that his interest in it had been "subject to all the UK taxes in the normal ways".
He paid income tax on dividends but the £19,000 profit on the sale was insufficient to attract capital gains tax.
The PM also repeated his willingness to publish his tax return - and make it the norm for premiers and Opposition leaders.
"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," he told ITV News.
However, he also conceded that he was not able to "point to every source of every bit of the money" that his father left him when he died - around £300,000 - when asked whether it was linked to investments in Jersey.
Shadow chancellor John McDonnell declined to join calls for the PM to resign over the issue but said there had been a "significant erosion of trust' in Mr Cameron, who still had questions to answer.
They included why he intervened to stop EU plans to force trusts to face the same transparency as companies, he added.
Mr McDonnell said: "There's significant erosion of trust in the Prime Minister because he wasn't straight and he didn't answer straight away and responses, as others have said, had to be dragged out of him.
"It's not a matter of resignation at the moment, it's a matter of making sure that the Prime Minister is straight with us."
The shadow chancellor, who published his own tax affairs at the start of the year, said it was important for senior ministers to do the same.
He said: "I think it's up to the individual politicians but if you're holding senior office, particularly in regards to the management of the economy, I think actually it's important that you do - that's why I published mine."
Scottish First Minister Nicola Sturgeon said that, while Mr Cameron had previously "talked a good game on tax avoidance, we've found out this week the reality doesn't always match the rhetoric".
She called for the Prime Minister to be "completely open and transparent" about the situation, but also demanded a thorough review of the tax regime in the UK.
Ms Sturgeon said: "I think David Cameron has given the impression that he's been trying to hide something over the past few days, he's had several statements and started by giving the impression there was nothing to hide before last night saying he had benefited from an offshore trust.
"I think he has to be completely open and transparent about this now."
She added: "More fundamentally perhaps it's time for a root-and-branch overhaul of tax avoidance rules in the UK. The whole system is complex, it's not transparent, and people don't really know who pays tax here and in what circumstances.
"What shocks people most about some of these schemes is they are not illegal. They're perfectly legal, but are they right? I think that's the question that now needs to be addressed."