While Israel is in negotiations with Palestinian Fatah, which holds sway in the Israeli-occupied West Bank, the group's main rival Hamas is in de facto control of Gaza.
Mahmoud Abbas, the Palestinian president and leader of Fatah, and the Israeli leadership have in recent months expressed doubts that a peace deal will be reached by January 2009, when George Bush, the US president, leaves office.
Livni, who is currently foreign minister in Israel's transitional government, won the leadership of the Kadima party last month after Ehud Olmert resigned his post amid a raft of corruption allegations against him.
She has until November 3 to put together a majority coalition government, and on Sunday she urged Israel's political parties to quickly reach a power-sharing deal.
"Creating political stability quickly is necessary not for political needs, but so that we can ... deal with the challenges from outside, economic and others," she said.
A general election would be held in Israel next year if Livni does not succeed in forming a coalition government.
Although Livni has wide support from the electorate, her opponent Benjamin Netanyahu, who leads the Likud party, is about even in current opinion polls.
Livni, who is leading the Israeli negotiating team in talks with the Palestinians, said that changes in leadership in the US and Israel must not derail the peace process.
"If we leave the negotiating rooms and look at the calendar, or think that a government is changing, or an administration is changing, and we have to reach something partial, something that doesn't offer a response to the genuine demands of the Palestinians and Israelis, that will be a mistake that we can't allow ourselves," she said.
The aim of the current negotiations is towards a full peace accord, rather than a series of partial agreements, Livni said, endorsing the Palestinians' view of the talks as an "all or nothing" affair.
"Nothing is agreed upon until everything is agreed upon," she said.
Livni did not describe what she favoured as a suitable deal for Israel.
"We agreed to handle the talks in the negotiating rooms, not in the headlines," Livni said.
In a newspaper interview last week, Olmert said that Israel would have to surrender its control of the West Bank or equivalent terriotory to the Palestinians, as well as east Jerusalem.