Israeli Prime Minister Benjamin Netanyahu and Palestinian President Mahmoud Abbas on Thursday resumed direct talks in Washington after a 20-month hiatus.
The talks are aimed at ending a six-decade conflict between the two sides within a year.
The first round of talks, hosted by U.S. Secretary of State Hillary Clinton, was held in the State Department building.
"You each have taken an important step toward freeing your peoples from the shackles of a history we cannot change and moving toward a future of peace and dignity that only you can create," Clinton said at the opening session of the direct talks.
"We understand the suspicion and skepticism" many felt about the process, she said, but the U.S. believed the Palestinian and Israeli leaders could succeed.
Solving the Israeli-Palestinian conflict was in the national interests of the U.S., she said, vowing her country would play the role of "an active and sustained partner in the process."
"We cannot and will not impose a solution. Only you can make the decisions necessary to reach an agreement and secure a peaceful future for the Israeli and Palestinian people," she added.
Netanyahu said any peace agreement must take into account the " genuine security needs" of Israel.
He said a true and lasting peace will be achieved only with " mutual and painful concessions from both sides."
Abbas said direct talks should lead to a peace agreement within one year.
He once again called on Israel to stop all settlement activities in the West Bank and lift the embargo on the people in Gaza.