George Mitchell reiterated Washington's support for a Palestinian state alongside Israel, in talks with the Israeli president and foreign minister.
Foreign Minister Avigdor Lieberman said the diplomatic process was at a "dead end" and a new approach was needed.
Mr Mitchell is due to have dinner with Mr Netanyahu later on Thursday.
He will then travel to the West Bank for talks with Palestinian leaders on Friday.
The US envoy has arrived in Israel to a changed political landscape, says the BBC's Tim Franks in Jerusalem.
Senior Israeli and Palestinian figures doubt each others' ability or will to come to a full peace deal, our correspondent adds.
Mr Netanyahu, of the right-wing Likud party, has not endorsed the creation of an independent Palestinian state.
'New approach'
Mr Mitchell's first meeting on Thursday was with President Shimon Peres.
He assured the president of Washington's "absolute and strong commitment" to Israel's security.
"We are committed to two states for two peoples living alongside each other in security and peace," Mr Mitchell said, according to a statement from Mr Peres' office.
Mr Peres told him that "no door to peace" had been closed and called 2009 a "decisive year in the Middle East".
However his upbeat tone appeared to contrast with the message from Foreign Minister Lieberman, who has rejected the previous Israeli government's pledge in 2007 to work towards a Palestinian state under then-US President George W Bush.
Mr Lieberman told Mr Mitchell that "the traditional approach has so far brought neither results nor solutions," the ministry said in a statement.
"The Israeli government will have to formulate new ideas and a new approach," Mr Lieberman added.
"We anticipate close co-operation and co-ordination with the US administration."
Iranian issue
Iran was also discussed at both meetings.
Mr Peres dismissed as "nonsense" speculation that Israel was planning to attack Iran over its nuclear programme.
He said the solution with Iran was "not military", and progress with Tehran depended on international co-operation.
Mr Mitchell is due to meet Mr Netanyahu, who leads a right-leaning coalition combining the centre-right, centre-left and far-right parties.
Mr Netanyahu has said the economy in the Israeli-occupied West Bank should be improved before progress on creating a Palestinian state is attempted.
He has said he intends to resume talks and co-operation to promote "economic peace".
Israel committed itself in 2003 to the establishment of a Palestinian state under the "roadmap" peace plan.
After meeting Israeli leaders, Mr Mitchell will hold talks with Palestinian Authority President Mahmoud Abbas and Prime Minister Salam Fayyad in Ramallah on Friday.
On Saturday, chief Palestinian negotiator Saeb Erekat reiterated his administration's position that, for peace talks to resume, Israel must declare its support for a two-state solution.
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