Jerusalem ? Israeli Foreign Minister Tzipi Livni wasted no time Sunday working to put together a new government, meeting with potential coalition partners even as outgoing Prime Minister Ehud Olmert formally resigned. Her ability to move fast in her first task could have far-reaching effects on Mideast peace talks.

Livni, who has gained respect for favoring peace deals with the Palestinians and Syria while distancing herself from the unpopular Olmert, would become Israel’s second female prime minister after Golda Meir, who served from 1969-1974.

A former lawyer and one-time agent in the Mossad spy agency, Livni has 42 days to form a government.

Olmert remains in office until a new government is approved by the parliament, and he has pledged to press ahead with peace efforts as long as he is premier. That in itself might push reluctant Israeli politicians to deal quickly with Livni.

Olmert’s dismal approval ratings approach single figures, and both those who favor an accord with the Palestinians and those who oppose it don’t want him to be the one who presents an agreement to the people.

She met leaders from the pivotal Shas Party Thursday, hours after she won a primary election to succeed Olmert as head of their Kadima Party. Over the weekend, she sat with leaders of several other factions, and later Sunday, she met with Defense Minister Ehud Barak, head of the Labor Party, Olmert’s main partner.

Olmert told his Cabinet on Sunday that he would resign and followed that with a visit to the Jerusalem residence of President Shimon Peres – both formalities in a process that began in late July, when Olmert caved under the pressure of corruption probes and announced he would step down after the Kadima primary election.