Prosecutors questioned American businessman Morris Talansky at the Jerusalem District Court, before the New York resident, who had been ordered by the court to extend his stay in Israel, returns to the United States.
Olmert, who was twice questioned by police in recent weeks, said earlier this month he took cash from Talansky for his two successful campaigns for mayor of Jerusalem in 1993 and 1998, a failed bid to lead the right-wing Likud party in 1999 and a further internal Likud election in 2002.
Both Olmert and Talansky have denied any wrongdoing.
Olmert, who has been holding talks with Palestinian President Mahmoud Abbas and has opened a negotiating track with Syria under Turkish auspices, has said he would resign if indicted.
Last week the Supreme Court rejected Olmert's appeal to prevent Talansky from giving preliminary testimony.
State Prosecutor Moshe Lador, said this month that investigators suspected Talansky had given Olmert "dollars, in cash and in envelopes, during brief meetings from time to time".
Olmert has said that his ex-law partner was responsible for overseeing the funds received for his election campaigns.
Israeli election law broadly prohibits political donations of more than a few hundred dollars. A judicial source said the sums involved totalled hundreds of thousands of dollars.
Legal experts have said investigators want to examine whether the money was reported to the proper authorities and if Olmert dispensed any favours in return for the cash.
A police source, who declined to be named, said last week that Israeli investigators would travel to the United States in the coming weeks to continue the investigation.