US Secretary of State John Kerry says he is confident difficulties between the Israelis and Palestinians can be overcome.
Mr Kerry has embarked on a new round of diplomacy to revive stalled peace talks in the Middle East.
During a meeting with Israeli Prime Minister Benjamin Netanyahu in Jerusalem, Mr Kerry said he believed progress could be made with good faith and a serious effort on both sides.
He also met with Palestinian Authority President Mahmoud Abbas in Bethlehem and plans to speak with both men several times during his visit.
Mr Kerry appealed for private negotiations behind closed doors, the BBC reports.
He also reaffirmed that the United States views Israeli settlements in the occupied Palestinian territory, the West Bank, as illegitimate.
Mr Netanyahu says Israel is abiding by the terms of the negotiations but accused the Palestinians of incitement and of creating artificial crises.
The Maan news agency has reported that Mr Abbas says the negotiations with Israel have not made any progress so far.