Israeli Prime Minister Benjamin Netanyahu, left, speaks as Palestinian President Mahmoud Abbas, right, and U.S. Secretary of State Hillary Clinton look on at the State Department in Washington, D.C., on Thursday. (Jim Young/Reuters)

Israeli Prime Minister Benjamin Netanyahu and Palestinian President Mahmoud Abbas have agreed to meet again following their first direct talks since December 2008.

The two leaders met in Washington, D.C., on Thursday at a meeting mediated by U.S. Secretary of State Hillary Clinton and George Mitchell, the U.S. Mideast peace envoy.

Flanked by Abbas and Netanyahu at the head of a U-shaped table in the State Department's ornate Benjamin Franklin room, Clinton said the Obama administration was committed to a settlement. She stressed, though, that the heavy lifting must be done by Netanyahu and Abbas with support from the international community, particularly the citizens of Israel and Arab countries.

Netanyahu and Abbas vowed to work together, but each outlined concessions required from the other.

"I see in you a partner for peace," Netanyahu told Abbas. "Together, we can lead our people to a historic future that can put an end to claims and to conflict. Now, this will not be easy. A true peace, a lasting peace, would be achieved only with mutual and painful concessions from both sides."

Abbas called on Israel to end Jewish settlements in the West Bank and other areas that the Palestinians want to be part of their own state. Netanyahu insisted that any agreement must ensure Israel's security as a Jewish state.

"We do know how hard are the hurdles and obstacles we face during these negotiations — negotiations that within a year should result in an agreement that will bring peace," Abbas said.

Calling Thursday's talks "productive," Mitchell told reporters that Netanyahu and Abbas plan to meet again on Sep. 14 and 15 in the Middle East, and roughly every two weeks after that.

Mitchell said he and Clinton will be at the second round of negotiations later this month, adding that a venue has not been chosen.

"I believe these two leaders, President Abbas and Prime Minister Netanyahu, are committed to doing what it takes to achieve the right result," Mitchell told reporters during a briefing while Thursday's meetings were still ongoing.

Declining to go into details, Mitchell said the talks touched on some of the core issues of the negotiations. Those issues include territories, security, Jerusalem, refugees, and settlements, as laid out at the opening of the day's talks by Clinton.

U.S. officials hope these talks will serve to ultimately produce an agreement within a year on the creation of a Palestinian state.

With files from The Associated Press