Foreign Minister Livni, elected leader of the centrist Kadima party last month, would take over as prime minister from Ehud Olmert, who resigned in a corruption scandal but remains in office until a new government is established.
At a meeting with President Shimon Peres, Livni requested and received an additional 14 days to try to finalise a governing coalition, a spokesman for Peres said.
From the outset, commentators had expected Livni would need a full six weeks to negotiate coalition deals.
"Yes, you need more time ... I am ready to help," Peres told Livni, who said at his office that she would "bring a government to life" to deal with the current period of economic instability.
"We can reach decisions and wrap things up," Livni said.
The question remains whether Livni, who has already won preliminary agreement from Defense Minister Ehud Barak's Labor Party to join a government under her leadership, can persuade the ultra-Orthodox Shas party to sign up.
With Labor in her corner, Livni would control 48 of the 120 seats in parliament. Shas's membership would boost that number to 60, a wafer-thin coalition but enough to block the opposition from toppling her government in no-confidence votes.
Winning the support of smaller factions, such as the Pensioners party, with seven lawmakers, and left-wing Meretz, with five, would give Livni a stronger mandate to pursue policies that include peacemaking with the Palestinians.
Shas, which has long billed itself as a party that represents
Negotiations between Kadima and Shas are likely to be stepped up, amid speculation that Livni intends to present a government when parliament reconvenes on Oct. 27 after its summer recess.
Without Shas, she could form a minority government relying on precarious support from outside the coalition of left-wing and Arab parties wary of a national ballot that opinion polls show Benjamin Netanyahu's right-wing Likud would win.
An early election, ahead of voting not due until 2010, would be likely should Livni fail to establish a government.