Shadow chancellor George Osborne has denied claims he tried to solicit a £50,000 donation for the Tories from Russian billionaire Oleg Deripaska.
Financier Nathaniel Rothschild said Mr Osborne discussed a donation from Mr Deripaska in the presence of a witness at his Corfu home in August.
The subject came up again later on the Russian's yacht, Mr Rothschild claimed.
Mr Osborne has denied this and he has been backed by David Cameron who said he had shown the "right judgement".
"I think it was the right judgement not to ask for any money and it was the right judgement for the Conservative Party not to take any money," Mr Cameron said.
Mr Rothschild alleged he had discussed the idea of a donation - first brought to a light in a letter to the Times on Tuesday - via Mr Deripaska's UK firm, LDV Ltd, three times with Mr Osborne and Tory fundraiser Andrew Feldman on August 24.
He said the first discussion, held in his Corfu home, was witnessed by a New York fund manager, James Goodwin.
This raises real questions about the Conservatives' judgement in pursuing allegations about Mandelson's dealing with a man who they themselves had discussed money with
He added that Mr Goodwin also "recalled" that the subject of a donation "arose briefly" later when the men were guests on Mr Deripaska yacht but the "conversation gained no traction".
Mr Rothschild said the subject was raised again with Mr Osborne in conversations later that evening at his house, 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".
The financier has said he will not "back down" over the allegations and is prepared to defend them in court.
Under electoral law, overseas residents cannot make donations to UK political parties.
In a statement to reporters outside Conservative campaign headquarters in central London, Mr Osborne denied seeking to solicit a donation, 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]."
He added that he had met Mr Deripaska on his boat on two occasions and that "on both occasions we didn't ask for money".
Mr Osborne, who said he had been with business secretary Lord Mandelson during one of the visits to the yacht, later released a chronology of the five occasions he had met Mr Deripaska this year.
This chronology makes clear that the possibility of a donation was discussed, but the Conservatives say the idea was raised by Mr Rothschild, and they had rejected the offer of a donation via LDV Ltd.
Mr Cameron later called on Mr Mandelson to give a detailed account of his own dealings with the Russian billionaire while Mr Osborne insisted he "completely stood by" his account of events.
Tory leader David Cameron voices his support for George Osborne
The Conservatives stated that "the allegations made in Mr Rothschild's letter to the Times are completely untrue".
"Both Andrew Feldman and George Osborne deny absolutely that they attempted to solicit a donation from Oleg Deripaska.
"Nor did they suggest a method by which he could conceal a donation via a British company.
"They spent a short period of time on Mr Deripaska's boat at the invitation of Mr Rothschild.
"Donations to the Conservative Party were not discussed with Mr Deripaska.
"In a conversation on September 18, Mr Rothschild suggested to Andrew Feldman that Mr Deripaska wanted to make a donation to the party through one of his British companies."
The statement added: "The offer was not taken up. For clarity - the Conservative Party has neither sought or received any donations from Mr Deripaska nor any of his companies."
BBC Business Editor Robert Peston said Mr Rothschild feels that Mr Osborne abused his friendship, by allegedly encouraging newspaper reports that embarrassed two of his other friends, Oleg Deripaska and Peter Mandelson.
Perhaps in future it would be better if all involved accepted the age-old adage that private parties are just that."
Fairly or not, according to the BBC's Peston, Mr Rothschild holds Mr Osborne partly responsible for media insinuations that Lord Mandelson, at the time Europe's trade commissioner, was guilty of a conflict of interest in accepting hospitality from Mr Deripaska on the magnate's super-yacht.
In his letter to The Times, Mr Rothschild said he was writing because of that newspaper's "obsession with Mr Mandelson".
He added: "I also think it ill behoves all political parties to try and make capital at the expense of another in such circumstances.
"Perhaps in future it would be better if all involved accepted the age-old adage that private parties are just that."
The Lib Dems said a "lot more questions" had to be answered about the affair and called for a parliamentary inquiry.
"I believe we need a full investigation and some light shed on the whole affair," home affairs spokesman Chris Huhne said.
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