Downing Street has been forced to further clarify David Cameron's financial affairs after questions about his family's tax arrangements.
No 10 said there were "no offshore trusts or funds" that the prime minister or his immediate family would benefit from "in future".
Labour say questions still remain and want him to publish his tax returns.
It comes after a row over an investment fund set up by Mr Cameron's late father Ian.
Leaked documents revealed Ian Cameron was a client of Panamanian law firm Mossack Fonseca and used one of the most secretive - albeit lawful - tools of the offshore trade after he helped set up a fund for investors.
Downing Street initially said Mr Cameron's tax affairs were a "private matter".
But after a day of questions from the media about whether his family retains an interest in the fund, Downing Street took the unusual step of issuing a statement saying Mr Cameron, his wife and his children "do not benefit from any offshore trusts".
And Mr Cameron himself said he had no shares or income from offshore trusts.
It followed a call from Labour leader Jeremy Corbyn for an independent inquiry into Britons linked to tax haven allegations - including Mr Cameron's family.
But there was criticism that Mr Cameron had not said whether he had already benefitted, or would gain in the future, from offshore funds.
In its latest statement, issued on Wednesday, Downing Street told the BBC: "There are no offshore trusts or funds from which the prime minister, Mrs Cameron or their children will benefit in future."
The statement did not address the issue of whether Mr Cameron had previously gained from his late father's investment fund - which Labour's Wes Streeting said needed clarifying.
"I think there are still questions about whether or not he benefited in the past," the MP, who sits on the Commons Treasury Select Committee, told BBC Radio 4 Today.
Labour MP Jess Phillips attacked David Cameron's late father for not "paying his fair share" of tax - saying it was "utterly disgusting," in a blog for the Huffington Post.
She said Mr Cameron "doesn't need our praise for paying his tax", adding: "He's not a very clever boy, he's a very average boy who used privilege rather than brains to get where he got."
By BBC Assistant Political Editor Norman Smith
Number Ten are clearly desperate to close down the ongoing story about the prime minister's tax affairs.
Hence, four statements in 24 hours.
But every time they close down one line of questioning - it simply opens up another one. Number Ten cling to the hope that the storm will blow over. But are they whistling in the wind?
Well, perhaps not.
Journalists may keep asking ever more intricate and detailed questions but will people still be interested?
Secondly, tax havens, offshore funds, bearer shares... it's all very complicated and perhaps a bit of a turn-off.
And finally it's a bit of a "Bullingdon" row.
Everyone knows Mr Cameron comes from a wealthy and privileged background.
Those that think this disqualifies him from being prime minister will probably continue to do so. Those that think it doesn't matter, will also probably continue to do so.
But London Mayor Boris Johnson, whose relationship with Mr Cameron has been strained by the EU referendum, defended the prime minister, dismissing the allegations about his financial affairs as "absolute tripe".
"The prime minister has made a very clear statement that he does not have a trust or any income from trusts and all the rest of it," he told LBC Radio.
Mr Corbyn said he would publish his tax returns and called on the prime minister to do the same.
Chancellor George Osborne said the government had done more than any previous government to tackle tax evasion and avoidance and to "make sure people pay the taxes that are owed".
Asked whether he himself had benefitted from an offshore fund, Mr Osborne said: "All of our interests as ministers and MPs are declared in the register of members' interests. We've made our position very clear."
A source close to the chancellor later said Mr Osborne "has no offshore interests, in shares or anything else" and had "made clear" his interests were "properly declared" in the register.
Business Secretary Sajid Javid, who is in India for talks with Tata Steel, was asked about his own financial affairs, and told the BBC: "I don't have any overseas trusts or overseas funds."
The prime minister is hosting an international anti-corruption summit in London in May as part of the government's transparency agenda.
Mr Cameron has said the government has reclaimed billions of pounds and led the world in having an open register of beneficial owners of companies, which is due to come into force in June.
He is facing calls to increase the pressure on tax haven UK overseas territories to fully open up their business registers to UK law enforcement agencies to improve transparency.
Labour has also called on the prime minister to consider taking "direct rule" of UK overseas dependencies and territories that do not comply with UK tax laws.