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.
David Chater, Al Jazeera’s correspondent in Jerusalem, said that if Kadima’s next prime minister fails to keep the coalition government together, early elections will have to be called and this could have a direct impact on ongoing peace talks with the Palestinians.
Ahmed Qurei, head of the Palestinian negotiating team with Israel, told Al Jazeera 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.”
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.