Talansky, a US businessman, allegedly gave funds to Olmert over a 15-year period [EPA]

Amir Dan, Olmert's spokesman, said that Friday's questioning lasted for three hours at his Jerusalem residence.

"The prime minister answered all of the investigators' questions," and "of his own volition".

Olmert suggested to add an extra hour of questioning, and that questioning would continue next week, Dan said.

Police are investigating suspicions that Olmert improperly accepted funds from Morris Talansky, a US businessman, who is alleged to have given Olmert at least $15,000 over a period of 15 years.

Another case involves alleged violations of rules in funding trips abroad.

While police have not yet charged Olmert, public outrage has damaged his approval ratings, and he announced on Wednesday that he would resign.

Benjamin Natenyahu, Israel's right-wing Likud party leader, called for fresh elections after Olmert pledged to resign following the announcement that his governing party, Kadima, would hold leadership elections on September 17 in the wake of his disapproval ratings.

Ahmed Qurei, head of the Palestinian negotiating team with Israel, said that the they were negotiating with Israel as a whole, not as individuals.

"Whether he [Olmert] is still the prime minister for two days or two months, we will continue to deal with him.

"If someone else comes, we will deal with them, as long as they want to deal with us."

Kadima contenders

Tzipi Livni, the Israeli foreign minister, is the main candidate for Kadima's chief position. Livni is Israel's chief negotiator with the Palestinians.

But the the deputy Israeli prime minister and transport minister, Shaul Mofaz, is closing the popularity gap.

Mofaz said in a speech on Friday that Israel's peace efforts with the Syrians should continue.

"My opinion and my goal will be to continue to speak to the Syrians without preconditions," "The way is - peace for peace," he said.

It could take months for Olmert's successor to form a new coalition, which means, according to Israeli officials, Olmert could remain caretaker prime minister for 100 days after he resigns.

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