Jeremy Corbyn has said it is in the Prime Minister's "own interests" to disclose details of his family's arrangements with offshore tax havens.
Mr Corbyn has challenged Downing Street's claim that the business affairs of Mr Cameron's late father Ian, which were disclosed in the Panama leak, were a private matter.
The Labour leader said: "I think the Prime Minister, in his own interests, ought to tell us exactly what's been going on."
Mr Corbyn said he wanted an investigation conducted by HM Revenue and Customs "about the amount of money of all people that have invested in these shell companies or put money into tax havens and to calculate what tax they should have paid over the years".
The financial watchdog ordered banks and businesses to check whether they have links to a law firm at the centre of the Panama Papers leak.
In a letter to the European Council President in 2013 Mr Cameron argued offshore trusts should not be subject to new transparency proposals.
The nature of the tax avoidance carried out by Blairmore Holdings may have been misunderstood.