JERUSALEM - Israel's corruption-tainted prime minister told his Cabinet on Sunday that he would step down, following through on a promise to allow the new leader of the ruling party to try to form a coalition government.

But Ehud Olmert did not say when he would formally submit a letter of resignation, leaving the exact timing of his departure unclear. Israel Radio reported that Olmert would hand the letter to President Shimon Peres later in the day, but the report could not be confirmed.

In televised remarks at the opening of Israel's weekly Cabinet meeting, Olmert said he would tell ministers of his "intention to resign the office of prime minister of the state of Israel."

He pledged to stand by Foreign Minister Tzipi Livni, who was elected last week to replace him as chairman of the governing Kadima Party. Livni has been busy in recent days lobbying potential partners to join a new coalition under her leadership.

"I wish Tzipi Livni luck in forming a government as quickly as possible," Olmert said. "I will be at her disposal and will help her with all my might to form a government."

Olmert is being forced from office by a series of police investigations into his financial dealings. He had promised to resign as soon as a new Kadima leader was chosen, and at a party meeting Friday, Livni pointedly brought up that pledge.

Even though she is now head of Kadima, Livni does not automatically become prime minister. Peres would have to first appoint her to try to put together a governing coalition -- something he is expected to do after Olmert formally resigns. After assigned that task, Livni would have six weeks to form a new government. Should she fail, new elections would be called for early 2009, a year and a half ahead of schedule.

Polls show that in the event of an election, Kadima would be in a tight race with the hawkish Likud Party, headed by opposition leader Benjamin Netanyahu, a former prime minister.

Over the weekend, Livni met with leaders of two small factions outside the coalition, hoping to shore up any government she could put together. Any accords that might emerge from talks with the Palestinians and recently renewed, indirect negotiations with Syria would benefit from broad-based parliamentary backing. The current government controls 67 of parliament's 120 seats.

Neither Kadima nor its coalition partners appear eager for a new election, fearing they would be ousted from power. But the ultra-Orthodox Shas Party, which could be key to building a new coalition, has already said it would not join a government willing to share Jerusalem with the Palestinians.

As lead peace negotiator, Livni is committed to discussing all the outstanding issues between Israel and the Palestinians. The fate of Jerusalem, whose eastern sector the Palestinians claim for a future state, is at the core of the conflict.

Kadima was founded in 2005 by then-Prime Minister Ariel Sharon. But Sharon suffered a debilitating stroke in early 2006, pushing Olmert into the leadership role.

Olmert led Kadima to victory in 2006 parliamentary elections. But his term in office was troubled by a series of police investigations, Israel's inconclusive 2006 war against Lebanese Hezbollah guerrillas and months of peace talks with the Palestinians that have yielded no breakthroughs.