Unless progress was made towards establishing a Palestinian state as mandated by a US-backed peace road map, Livni said in a speech on Monday, pressure could grow to turn Israel into a bi-national state in which Israelis and Palestinians would share power.
With a higher Palestinian birth rate, that could mean the end of a Jewish majority in what is now Israel, she said, giving voice to an argument Ehud Olmert, the interim prime minister, has raised for trading occupied land for peace.
Livni said: "I say that time works to our disadvantage, not only from the standpoint of demographic numbers ... but also from the standpoint of the legitimacy of a state for the Jewish people in the eyes of the international community."
"[Israel should not] sit and look to stagnation as a kind of solution, but try to find solutions"
Israel's foreign minister
She stopped short of urging a quick resumption of stalled peace talks, but said Israel should not "sit and look to stagnation as a kind of solution, but try to find solutions".
Livni, a former official in the Mossad intelligence service, is widely seen in Israel as a rising political star. She is number two behind Olmert in Kadima, the centrist party founded by Ariel Sharon, who was incapacitated by a stroke on 4 January.
Opinion polls predict Kadima will win national elections in Israel on 28 March.