"It is crucial to understand that Israel, with the international community, expects any Palestinian government to meet these requirements fully and completely," Livni added.
Rice said the United States would await the formation of the unity government before passing judgment.
"We are between the announcement of the intention to form a government and the actual formation of that government," she said
Rice arrived in Israel on Saturday for meetings with Israeli and Palestinian leaders aimed at reviving the Middle East peace process.
The US secretary of state was travelling from Iraq, where she made a surprise visit earlier in the day to review the latest operation to pacify the war-torn capital and urged progress on political reconciliation.
Following her talks with Livni, Rice is due to have one-on-one meetings on Sunday with Olmert in Jerusalem and later with President Mahmoud Abbas in Ramallah.
The secretary of state's visit will culminate on Monday in a three-way meeting with, Abbas, and Olmert.
Rice has said that during Monday's meeting she hopes to move beyond security issues which have bogged down Israeli-Palestinian negotiations for years and get the two sides talking about the contours of a future Palestinian state.
Deal with it
The Palestinian president met with a senior US State Department official on Saturday to discuss the emerging unity government.
The official, David Welch, informed Abbas that Washington would boycott all members of the coalition, including those from Fatah, unless it falls into line with international demands, but would decide its position only when the new coalition takes office, according to Abbas' aides.
Palestinian officials said for his part the president told Mr Welch that the new coalition was something the world would have to deal with.
The incoming Palestinian unity government and its stance on key conditions are likely to top Monday's three-way talks, with Israel warning Abbas that any failure to live up to the three demands of the Middle East quartet (The US, EU, UN and Russia) will only spell more isolation for the beleaguered Palestinian Authority.
But Abbas has also insisted that the Quartet accept the power-sharing agreement signed in Mecca on February 8 under the auspices of the Saudi King Abdullah, which paved the way for the incoming unity government between Abbas' Fatah faction and Hamas.