JERUSALEM (Reuters) - Israeli Prime Minister Ehud Olmert handed his resignation to President Shimon Peres on Sunday but the scandal-hit premier could stay in office for weeks or months until a new government is formed.
"Prime Minister Ehud Olmert submitted his resignation to me tonight," Peres told reporters at his Jerusalem residence.
Olmert, who faces criminal indictment in corruption probes, said earlier at the weekly cabinet session he was stepping down "in accordance with good governance" and history would judge the achievements of his administration.
Peres said he would hold talks with all of Israel's 13 parliamentary factions before formally asking a consensual faction leader to form the next government.
Olmert was replaced by Foreign Minister Tzipi Livni as leader of the ruling Kadima party in an internal election on Wednesday, raising her chances of becoming Israel's first woman prime minister since Golda Meir in the 1970s.
Olmert's spokesman Mark Regev said the outgoing premier would stay on as interim prime minister until a new prime minister was sworn in.
"There cannot be a power vacuum," Regev said.
Olmert met with Livni and promised her his full support.
The political uncertainty has dimmed even further prospects of an Israeli-Palestinian peace deal which the United States had hoped Olmert and Palestinian President Mahmoud Abbas could achieve this year.
Peres will on Sunday hold talks with leaders of the four largest parliamentary factions -- Kadima, Labour, Likud and Shas -- and on Monday he will meet the remaining factions before he flies to New York to attend the 63rd opening ceremony of the United Nations General Assembly.
Olmert had promised to resign once a new Kadima chief was chosen.
If Livni, Israel's chief negotiator in peace talks with the Palestinians, gets the nod from Peres to try to form a new government, she will have up to 42 days to put together a coalition.
Failure to build a coalition would lead to an early parliamentary election.
Livni appeared to face an uphill battle to retain a political partnership with Defence Minister Ehud Barak's Labour Party.
In a snub to Livni, Barak met opposition leader Benjamin Netanyahu of the right-wing Likud on Saturday to discuss the political situation.
Political commentators said it appeared both men were trying to work out a deal for an early election and by keeping Olmert on as caretaker prime minister, freeze Livni out of the top leadership spot before a national ballot.
Opinion polls predict Netanyahu would win a general election, amid speculation he would keep Barak as defence chief.
(Additional reporting by Joseph Nasr)