She added that the USA would not back resolutions condemning Israel, like the one passed in December that called for the end of settlement building.
"What we are saying is let us not just talk about the old way of doing things, lets come to the table with all the fresh atmosphere perspective that we now have and see how can we move forward", she said.
"I think first of all a two-state solution is what we support", she said.
"If Israelis and Palestinians are able to achieve a two-state solution, I would be delighted", he said, noting there was no "appetite among Palestinians" for a one-state solution.
"I'm looking at two-state and one-state, and I like the one that both parties like".
Haley, 45, said: what we support more is peace and stability and by bringing the two to the table to have them talk through this in a fresh way, to say we are going to go back to the drawing board, what can we agree on, that is what the U.S. wants.
Ayrault pointed to Trump's remarks in a joint appearance with the Israeli prime minister, Benjamin Netanyahu, in which he explicitly abandoned the two decades-long U.S. commitment to the creation of a Palestinian state alongside Israel as part of a final peace deal.
That statement was seen as a break from previous U.S. policy and from the global consensus on recognition of a Palestinian state as part of a final Middle East peace deal.
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"We consider that the two-state solution has never been so threatened and yet so necessary", France's U.N. Ambassador François Delattre told reporters. "We are committed to this process, and we believe that this is the shortest distance to putting an end to this conflict", Mansour added.
She also insisted on calls to halt the construction of settlements in the West Bank, including East Jerusalem, and to immediately, unconditionally and completely lift the cruel and unlawful blockade on the Gaza Strip.
The Security Council earlier heard the United Nations envoy for the Middle East peace process, Nickolay Mladenov, insist that the two-state solution remains "the only way" to meet the aspirations of the Palestinians and Israelis.
While taking with reporters Thursday, Haley also accused the United Nations of having an anti-Israel bias.
He did not give details about the option that Tillerson raised and the secretary of state did not take press questions, but he appears to have echoed Trump's remarks suggesting other outcomes would be acceptable to the US.
"For those that don't have our back, we're taking names", she said then.
She said "outrageously biased" resolutions from the Security Council and General Assembly have made peace harder to reach, "by discouraging one of the parties from going to the negotiating table".