"The question is not to know who will be a member of this government, but what it will do and if it will accept the international community's three conditions -- renounce terrorism and violence while recognising Israel and past (peace) deals," Livni told public radio.
"For 11 months, the world stood firm, making it understood to Hamas leaders that they will not be able to hold on to their ideology, remain in power and continue to receive (international) funds while benefiting from international legitimacy," she said.
Livni spoke from Los Angeles, where she and a number of Israeli ministers were attending the 75th congress of American Jewish communities.
Her comments came a day after feuding Palestinian factions agreed, after five months of deadlock, that Mohammed Shbeir, a biologist and former head of the Islamic University in Gaza, would head a new unity government, replacing Ismail Haniya of the Islamist Hamas movement.
After Hamas formed a cabinet in March, the West suspended direct aid to the Palestinian government demanding that the movement, considered a terrorist organisation by the European Union and the United States, renounce violence, recognise the Jewish state and agree to abide by past peace deals.
The Palestinians hope that a new coalition cabinet will lift the aid freeze, which has led to unprecedented financial and political crisis in the beleaguered territories.
Born in 1946, Shbeir has a doctorate in clinical biology from the University of West Virginia. Perceived as a Hamas sympathiser although never a party member, he served as head of the Islamic University from 1993 until September 2005 when he retired to pursue his research.

Copyright AFP (Agence France-Presse), 2006