The United States and Israel have signed an agreement aimed at assuring Israel that the Palestinian group Hamas will not be able to re-arm if it agrees to a ceasefire in Gaza.
Ms Rice told reporters that the "memorandum of understanding" which she and Ms Livni intended to sign was "one of the elements" that could help bring about a durable ceasefire.
The US Secretary of State, Condoleezza Rice, and the Israeli foreign minister, Tzipi Livni, met in Washington to conclude the deal.
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