Hundreds of thousands of Palestinians fled or were driven out by Israeli forces in the 1948 Middle East war that followed the establishment of Israel and in 1967.
Many Palestinian refugees, the world's largest refugee population, remain in squalid camps in neighbouring Arab countries. The right of return for them and their descendants has remained a key demand within the peace process.
In her speech to the UN General Assembly on Wednesday, Livni said Israel believed in a vision of two states, Israel and Palestine, and that Israel had no wish to govern over Palestinians.
She said such a solution required that each state should be the solution for its own refugees, Israel as a homeland for Jewish refugees from around the world, and the future state of Palestine the answer for Palestinian refugees.
Livni said: "This is the real and only meaning of the two-state vision. It requires each people to accept that their rights are realised through the establishment of their own homeland, not in the homeland of others.
"If Palestinian leaders are unwilling to say this, the world should say it for them. Instead of giving false hope, it is time to end the exploitation of the refugee issue."
Right of return
Livni met Mahmoud Abbas, Palestinian president, on the sidelines of the UN session on Monday, and told the General Assembly that they had agreed "to re-energise the dialogue between us, and create a permanent channel to pursue ways to advance together".
But she said: "We have no illusions about the difficulties before us," adding that the Palestinian Authority was dominated by the Hamas movement "that teaches children to hate and seeks to transform the conflict from a resolvable political dispute into an endless religious confrontation."
Quartet backs Abbas
The Quartet of Middle East peace mediators have endorsed Abbas's effort to establish a national unity government with Hamas, which is still officially committed to the destruction of Israel.
In a statement, Kofi Annan, the UN secretary-general, and foreign ministers of the United States, European Union and Russia said: "The Quartet welcomes the efforts of Palestinian president Mahmoud Abbas to form a government of national unity, in the hope that the platform of such a government would reflect Quartet principles and allow for early engagement."
Abbas is trying to build a coalition of his Fatah movement and the Hamas movement which defeated it in elections in January.
The Quartet has boycotted the Hamas-led government formed in March because it refused to recognise Israel and renounce the resistance.
The use of the term "reflect" allows Abbas some leeway for what may be an oblique formula for recognising past Palestine Liberation Organisation agreements.
The statement, endorsed by Condoleezza Rice, US secretary of state, represented a significant softening of the United States' stance towards the Palestinian Authority since Hamas took it over this year and a diplomatic victory for the Europeans and UN, EU diplomats said.
Alvaro de Soto, UN Middle East peace envoy, said it would have been unthinkable three or four months ago, but "now there is the willingness to consider the possibility of a coalition government including Hamas".
The statement called for a three-month extension and expansion of a temporary mechanism that channels aid to the Palestinians bypassing the elected government.
The Quartet indirectly criticised Israel for maintaining its closure of the Gaza Strip and restrictions on Palestinians' freedom of movement in the occupied West Bank.
The US-led aid embargo and a ban on contacts with the Hamas-led government has contributed to worsening poverty and lawlessness in the Palestinian territories.
Benita Ferrero-Waldner, European external relations commissioner, said she wanted to see the temporary aid mechanism expanded "as much as we can" to ease the economic hardship among Palestinians.