"Thank you for your courage and commitment," US Secretary of State Hillary Clinton told Israeli Prime Minister Benjamin Netanyahu and Palestinian president Mahmud Abbas as she opened the negotiations.

"I know the decision to sit at this table was not easy," the chief US diplomat said at a rectangular table in a chandelier room at the State Department, flanked by the two leaders and their delegations.

But after a day of weighty symbolism and lofty rhetoric at preparatory meetings with President Barack Obama at the White House, Netanyahu and Abbas began sharpening their points and presenting opening demands.

"We expect you to be prepared to recognize Israel as the nation state of the Jewish people," Netanyahu told Abbas, as the two sat on either side of Clinton with their national flags behind them.

The point is likely to prove sticky for Abbas's delegation which may fear it will undermine the right-of-return claims for those Palestinians who left or fled Israel when it was created in 1948.

In the wake of two Palestinian militant attacks on settlers in occupied West Bank, Netanyahu also renewed references he made at the White House on Wednesday to protecting Israel's security.

"A real peace must take into account the genuine security needs of Israel," Netanyahu said.

Abbas appeared conciliatory on the security front.

"We consider security as essential and vital both for us and for you and we will not accept that anyone commits any act that would harm your security or ours," the Palestinian leader said.

He also said that investigations into the shootings that killed four Israeli settlers on Tuesday were progressing.

But he also stuck to his demands on settlements.

"We call on the Israeli government to move forward with its commitment to end all settlement activity and completely lift the embargo over the Gaza Strip," Abbas said.

Israel tightly controls access and egress from the Gaza Strip, which is run by the militant Hamas group, a rival of Abbas's Palestinian Authority and a sharp opponent of the peace talks.

The two Middle East leaders poignantly shook hands, and then Abbas appeared to give Netanyahu a thumbs up.

The leaders then went behind closed doors to begin tackling the core issues that have bedeviled past peace attempts -- Israel's security, borders of a Palestinian state, the right of return for Palestinian refugees and the fate of Jerusalem.

US Middle East envoy George Mitchell said that he, Clinton, Abbas and Netanyahu met for 90 minutes, with the two leaders pledging to work together to maintain security and reiterating their goal of a two-state solution.

The three-way meeting was "long and productive," Mitchell said, adding the leaders pledged to work in "good faith" and with "seriousness of purpose."

He said Netanyahu and Abbas then went off on their own for a one-on-one meeting, which may be designed to build trust between the two leaders. There were no note takers or translators in either of the meetings.

The two leaders also agreed to resume their talks on September 14-15 in the Middle East, planning to meet every two weeks thereafter, Mitchell said.

Mitchell said the two leaders agreed that a logical next step would be to start working on a "framework agreement" that would lead to "a comprehensive treaty that will end the conflict and establish a lasting peace."

He said the parties agreed the task could be done in one year.

Mitchell, a former troubleshooter in Northern Ireland who has a reputation as a dogged mediator, has said he is prepared to intervene with "bridging proposals" if needed and appropriate during the planned year of talks.

The Palestinians want to build a state in the West Bank and the Gaza Strip, which is currently run by the rejectionist Hamas movement, with east Jerusalem as its capital. Israel claims all of Jerusalem as its undivided capital.

Abbas had previously refused to enter direct negotiations without a full halt to Israeli settlement activity, but yielded under pressure from Obama.

But Abbas has warned that a renewal of settlement activities after September 26, when a 10-month partial moratorium expires, would end the negotiations. The settlements house about 500,000 people on lands occupied by Israel in 1967.

Netanyahu faces pressure from his Likud party to continue settlement construction.

The last direct peace negotiations ended in December 2008 when Israeli forces invaded Gaza to halt Hamas rocket fire on Israel.