"I believe I represent most Israelis and I can confirm that Gaza is not the last move. We are convinced that in order to establish a Palestinian state we must withdraw from additional territories," the minister added.
Livni, who gave the interview during a visit to Cairo this week, said that Israel was not interested in continuing to control the Palestinians.
"The majority of Israeli people not only understand the need for peace, but also the need to reach compromises in order to reach peace.
"In this context I represent the opinion of the majority, which supports a solution of two states, one for Jews and one for Palestinians, and this means that the road to a Palestinian state begins by renouncing terror – something which I believe represents not only Israel's interest, but also the Palestinians' interest.
"Israel made a number of concessions and took some courageous steps, like in our pullout from the Gaza Strip and in the removal of all the settlements. Thus, we conveyed a message to the Palestinians that we mean what we say," Livni said.
The foreign minister rejected the interviewer's claim that Gaza was a burden on Israel.
"When I decide to uproot 7,000 settlers from their homes, many of whom were born in Gaza, it is untrue to say that their presence there was a burden on Israel. Believe me, this decision was a courageous, difficult and painful decision.
"The goal was to convey a message to the world and the Palestinians that we are serious. At the same time, we wanted to say that we do not wish to control the Palestinians," Livni said.
She added that the decision to withdraw from the Strip derived from a vision of peace.
"What held up the peace process was not Israel's unwillingness, but the inability of the moderate Palestinian who believe in a two-state solution to control violence."
'Big difference between our image and reality'
"I don’t like answering questions which begin with 'if,' but in a situation where this is not implemented we will find the best ways to defend the State of Israel," she replied.
Livni refused to address her desire to run for prime minister, but referred to the claims that Israeli spies were operating in Egypt.
"Regarding the remarks on espionage, some of them are far from reality, but what is important is to focus on work in order to find a common denominator. I believe that we must change the public opinion's prejudice against Israel.
"Unfortunately, there is a big difference between Israel's image and reality, and this constitutes an obstacle on the way to peace. I know that not only in Egypt, but in other places in the world as well, Israel is still THE enemy and Israelis are working to control the Palestinians, and this is not true," she said.
"I want to take this opportunity and appeal to the Egyptian public opinion in a way that will express the stance and feelings of the Israeli public opinion. Egypt and Israel have a peace agreement, and out of that we want to reach real peace with Egypt and honor its status in the Arab world. Israel is ready and wants to reach compromises it was not ready to reach in the past," the foreign minister added.