Speaking a day after fighting Palestinian factions agreed in Mecca to form a government of national unity, Livni said Israel wanted a peaceful solution to the decades-old conflict.
"Peace is, I believe, feasible and achievable," she told the opening dinner at a major international security conference in Munich with top politicians from around the world. "But our desire to make peace cannot come at the cost of risking our very lives."
She said Islamist group Hamas, which won elections last year, did not represent the "national Palestinian interest or aspiration" but sought to destroy Israel.
Hamas has been feuding with Palestinian Authority Chairman Mahmoud Abbas's long-dominant Fatah movement over the shape of the government for months.
She said the principles of renouncing violence and acknowledging Israel's existence, as demanded by the Quartet of Middle East peace mediators - the United Nations, European Union, Russia and United States - were necessary for peace.
"These principles are crucial especially today when the eyes of the free world are looking at Mecca," she said.
Israeli officials said the unity government deal failed to meet Western conditions to end the sanctions imposed on the Hamas-led government.
Livni, who drew attention to Munich as being the site of the 1972 Olympics when Palestinian militants kidnapped a group of Israeli athletes and later killed 11 of them, also said nations should be firm with Iran over its nuclear program and support for militant Hezbollah in Lebanon.
Clearly referring to Iranian President Mahmoud Ahmadinejad, who called for Israel to be wiped off the map, Livni said: "It is a regime which mocks the Holocaust while threatening the world with a new one."