JERUSALEM (AFP) - Israel's scandal-tainted Prime Minister Ehud Olmert resigned on Sunday, setting the stage for more weeks of political turmoil as the horse-trading begins to form a new government. Olmert, who is battling a swathe of corruption allegations, handed a brief letter to President Shimon Peres announcing that "in line with his commitments, he is submitting his resignation," the President's office said. Peres, who now has a week to designate the party leader who will form the next govt, paid tribute to Olmert for his work "for the people and the state of Israel." Foreign Minister Tzipi Livni, who replaced Olmert as head of the centrist Kadima party in a leadership vote on Wednesday, is hoping to become only the second woman Prime Minister. "I have decided to end my functions as Prime Minister of the government of Israel," Olmert, who has been in power for 31 months, told a cabinet meeting earlier on Sunday. Olmert's move initiates what could be a months-long process to form a new govt, casting a shadow over peace talks with the Palestinians and further denting hopes of a deal by the end of this year. Peres was due to hold talks with Kadima representatives later Sunday, the local media said. The 62-year-old Olmert, who is likely to stay on as interim premier, had first announced on July 30 he would step down to battle a number of corruption allegations. Police have recommended criminal charges against him in two cases where he is accused of accepting large sums of cash from a US financier and multiple-billing foreign trips. He has denied any wrongdoing. Peres is expected to give Livni 42 days to form a govt and try to prevent a snap general election, which opinion polls indicate would bring the right-wing Likud party headed by ex-PM Benjamin Netanyahu to power. The Kadima leadership result confirmed Livni's meteoric rise to become the most powerful woman in Israel, and could now see her follow in the footsteps of Golda Meir, the country's first woman Prime Minister. But the turmoil unleashed by the allegations dogging Olmert also threatens to derail the US-backed peace talks with the Palestinians that were formally relaunched last November but have made little tangible progress since. As Foreign Minister Livni was lead negotiator for Israel in the talks. Both sides remain deeply divided on core issues, however, including final borders, Jewish settlements in the West Bank, the future status of Jerusalem and the fate of some 4.6 million Palestinian refugees.