Mr Talansky raised thousands of dollars at meetings in New York
A US businessman has testified he gave envelopes full of cash to Israel's prime minister but said he did not seek or receive any favours in return.
Morris Talansky told an Israeli court he did not know how the money was spent, but linked it to Ehud Olmert's "love" of "expensive" luxury goods.
Police are investigating whether the PM took up to $500,000 (£250,000) in bribes or illegal campaign donations.
Mr Olmert says sums from Mr Talansky were legal campaign contributions.
Mr Talansky made his claim during testimony under oath at the request of prosecutors, before his expected return to the United States.
"I gave [Mr Olmert] cash in envelopes," the millionaire campaign fundraiser said, according to a transcript of the hearing.
"I asked him why I couldn't write a cheque and he said it's because of the way the money is channelled."
When asked how the money was spent by Mr Olmert, Mr Talansky said: "I only know that he loved expensive cigars. I know he loved pens, watches. I found it strange."
Mr Talansky has already said that he gave Mr Olmert money for more than 10 years before he became Israeli prime minister.
Correspondents say the revelations are likely to damage further Mr Olmert's already low standing.
This is the fifth investigation that police have launched into the financial affairs of Mr Olmert, who also faced criticism about the handling of the 2006 war in Lebanon.
Mr Talansky told the hearing that the bulk of the money was raised in New York "parlour meetings", where Mr Olmert would address US donors who would then leave contributions on their chairs.
"He was articulate, he was intelligent. I felt that he would be a leader that I would have hoped to be if I had the talent," Mr Talansky said.
He also said that he had given Mr Olmert loans of tens of thousands of dollars for foreign trips, but the money was not repaid.
"I had a very close relationship with him, but... I never expected anything personally. I never had any personal benefits from this relationship whatsoever."
Mr Olmert has twice been questioned by police in recent weeks, but he has not been charged with any wrongdoing. He says he will resign if indicted.
Mr Talansky's testimony is not part of a trial but was taken as a precaution in the event of a future legal case, as he resides in the US and might not return to Israel.
Investigators reportedly want to examine whether Mr Talansky's donations were properly registered and if he received any favours as a result of the contributions.