David Cameron has repeated his support for shadow chancellor George Osborne saying he was "right" not to ask for any money from a Russian billionaire.
Gordon Brown has called for an investigation into claims George Osborne tried to solicit a £50,000 donation from Oleg Deripaska.
The Conservatives deny claims Mr Osborne tried to solicit a £50,000 donation from Oleg Deripaska.
The Tories firmly deny the allegations against the shadow chancellor.
But financier Nathaniel Rothschild says he did discuss a donation in front of a witness at his Corfu home in August.
Party leader David Cameron said Mr Osborne was "right" not to ask for money from the Russian billionaire.
Mr Osborne has also denied claims that he asked about ways to get round a ban on overseas donations to UK parties.
But speaking at prime minister's questions, Mr Brown said: "This is a very serious matter indeed and I hope it is investigated by the authorities."
Speaking outside his home on Wednesday morning, Conservative leader Mr Cameron said: "What matters is what you do and what you say and George Osborne was right not to ask for any money, the Conservative Party was right not to accept any money.
"And I think we have been right to set out in full all the meetings and everything that took place and others should do the same."
Yacht
But Labour MP and chairman of the Public Administration Select Committee Tony Wright said Mr Osborne had actually made a "fundamental misjudgement".
"The simple fact is once the issue of donations arose in the context of a foreign billionaire, George Osborne should have run a mile and not sought to get closer," he said.
Mr Rothschild has said he will not "back down" and is prepared to defend his claims in court.
He alleged he had discussed the idea of a donation via Mr Deripaska's UK firm, LDV Ltd, three times on 24 August - with Mr Osborne and Tory fundraiser Andrew Feldman.
He said the first discussion, held in his Corfu home, was witnessed by a New York fund manager, James Goodwin.
He said Mr Goodwin also "recalled" that the subject of a donation "arose briefly" later when the men were guests on Mr Deripaska's yacht but the "conversation gained no traction".
'More questions'
Mr Rothschild said the subject was raised again with Mr Osborne later that evening, in which he said the shadow chancellor was "interested in whether and how such a donation could be secured".
Furthermore, he added that during a conversation with Mr Feldman in the middle of September, he was "left with the impression that the Conservative Party remained interested in pursuing it".
On Tuesday, Mr Osborne denied asking for any money, but did not rule out having discussed a donation.
He said: "People make suggestions all the time about donations to the Conservative Party, but we are always clear and rigorous [in assessing these]."
The Conservatives say the possibility of a donation was raised by Mr Rothschild, but any suggestion that money could be routed through LDV Ltd was rejected.
The Lib Dems said a "lot more questions" had to be answered about the affair and called for a parliamentary inquiry.
Former Chair of the Committee on Standards in Public Life, Sir Alistair Graham, told the BBC it showed party funding continued to be an "awkward issue" for all parties adding: "Politics never stops surprising you about how nasty it can get."
