Livni and Yitzhak Molcho are representing Israel in peace talks that began this week in Washingon with Palestinian negotiators Saeb Erekat and Mohammed Shtayyeh.
The talks are expected to resume in about two weeks in Israel or the West Bank as part of a nine-month commitment by both sides to tackle the contentious so-called final-status issues needed to create a Palestinian state.
"We are not entering this process euphoric or with the expectation of a new Middle East -- we see the changes in the region," Livni, Israel's justice minister, told Ynetnews.com Wednesday.
"This process creates a partnership that is highly important to us ... we have an opportunity to form an alliance against extremist threats, The goal is to reach a settlement -- not just hold negotiations," she said.
Security and future borders must be discussed before moving on to final status issues, Palestinian President Mahmoud Abbas said.
U.S. Ambassador to Israel Dan Shapiro said he was optimistic the new peace talks would succeed.
"Clearly there is good reason to be skeptical because of what we have seen in the past. But there is also reason for hope and a possibility of success and it is worthwhile for everyone to support the brave leaders who have taken this path," Shapiro said in an interview on Israel Radio.
Issues include determining a future Palestinian state's borders, security arrangements for both countries and the fate of refugees displaced by Israel's creation in 1948 and the 1967 Arab-Israeli war.
President Barack Obama, who met with the negotiators at the White House Tuesday, gave each team a letter outlining the U.S. position on two of those points, Israeli newspaper Haaretz reported.
The letter said the administration believes the starting point for peace talks should be the prevailing borders before the 1967 war, adjusted with mutually agreed land swaps to account for Israeli West Bank settlements, the newspaper said.
In the Six Day War, Israel took effective control of the Gaza Strip and the Sinai Peninsula from Egypt -- known then as the United Arab Republic -- the West Bank and East Jerusalem from Jordan and the Golan Heights from Syria.
Obama's letter to Israel included a U.S. declaration that Israel is a Jewish state and the Obama administration believes the displaced Palestinian refugees should return to the future Palestinian state, Haaretz said.
Responding to the report, the White House said, "We don't comment on presidential correspondence."
A senior White House official stressed Obama was "closely engaged ... every step of the way" in the peace process led in recent months by Secretary of State John Kerry.
"The president kick-started the process during his trip to the region in March," the official told reporters.
Obama first declared the U.S. position on the borders in May 2011.
"It is a well-known formula to all who have worked on this issue for a generation," Obama told an influential American-Israel lobbying group May 22, 2011. "It allows the parties themselves to account for the changes that have taken place over the last 44 years.
"The ultimate goal," he said, "is two states for two peoples -- Israel as a Jewish state and the homeland for the Jewish people and the state of Palestine as the homeland for the Palestinian people, each state enjoying self-determination, mutual recognition and peace."
Before meeting with Obama, Israeli and Palestinian negotiators held extensive talks with Kerry at the State Department.
At the talks' conclusion, Livni, Israel's chief negotiator and a proponent of the two-state solution, and Erekat appeared with Kerry at a State Department news conference.
Erekat thanked Obama and Kerry for their "relentless efforts and unwavering commitment to achieve a just, comprehensive, lasting peace between Palestinians and Israelis."
"Palestinians have suffered enough, and no one benefits more from the success of this endeavor more than Palestinians," he said. "I am delighted that all final-status issues are on the table and will be resolved without any exceptions. It's time for the Palestinians to live in peace, freedom and dignity within their own independent, sovereign state."
Livni said, "In these negotiations, it's not our intention to argue about the past, but to create solutions and make decisions for the future."