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Each of the leaders pledged to work diligently toward peace
US President Barack Obama has urged Israeli and Palestinian leaders not to let the chance of a permanent peace deal "slip away".
"This moment of opportunity may not soon come again," he said, pledging US support for the new negotiations.Mr Obama spoke the day before a new round of direct talks between Israeli PM Benjamin Netanyahu and Palestinian leader Mahmoud Abbas was due to begin.
Earlier, he condemned the "senseless slaughter" of four Israeli settlers.
They were shot dead by gunmen near
the West Bank city of Hebron on Tuesday, with the armed wing of
Islamist movement Hamas, which controls the Gaza Strip and opposes peace
talks with Israel, saying it had carried out the attack.
And in another attack, two Israelis were shot and wounded on
Wednesday in the West Bank at Rimonim Junction, near the Jewish
settlement of Kochav Hashahar.Mr Obama spoke at the White House on Wednesday evening after meetings with Mr Netanyahu, Mr Abbas, Jordan's King Abdullah II and Egyptian President Hosni Mubarak.
His remarks came on the eve of the first direct negotiations between Israeli and Palestinian leaders in 20 months, which he said were "intended to resolve all final status issues".
'Partners in peace' Mr Obama said the goal of the talks, which are expected to last a year, was a permanent settlement that ended the Israeli occupation that began in 1967 and resulted in an independent, democratic Palestinian state existing peacefully beside Israel.
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He will have been pleased by what seemed to be a warm handshake between the Palestinian President Mahmoud Abbas and the Israeli Prime Minister Benjamin Netanyahu.
Even so, Mr Abbas is still insisting that Israel must stop building homes for Jews in the occupied Palestinian territories.
Mr Abbas has threatened to walk out of the talks on the settlement issue. It's not clear where the compromise will come from. Warm words alone won't do it - but perhaps Mr Netanyahu's were a start.
There might not be room for many more failures. The conflict is changing. A religious war is now being grafted on what used to be fundamentally a competition for territory between two national movements. You can make deals with nationalists. It's much harder with people who believe they're doing God's work.
Analysis
President Obama has started what will be an intensive diplomatic push.He will have been pleased by what seemed to be a warm handshake between the Palestinian President Mahmoud Abbas and the Israeli Prime Minister Benjamin Netanyahu.
Even so, Mr Abbas is still insisting that Israel must stop building homes for Jews in the occupied Palestinian territories.
Mr Abbas has threatened to walk out of the talks on the settlement issue. It's not clear where the compromise will come from. Warm words alone won't do it - but perhaps Mr Netanyahu's were a start.
There might not be room for many more failures. The conflict is changing. A religious war is now being grafted on what used to be fundamentally a competition for territory between two national movements. You can make deals with nationalists. It's much harder with people who believe they're doing God's work.
He said the US could not impose peace on the two parties, and that the US could not want peace more than them.
And he praised Mr Abbas and Mr Netanyahu as leaders "who I believe want peace".But he warned of "extremists and rejectionists who, rather than seeking peace, are going to be seeking destruction."
In remarks ahead of a Wednesday evening dinner with the Arab leaders, Mr Netanyahu described Mr Abbas as his "partner in peace", and said he would not allow the latest attacks to "block our path to peace".
"Our goal is to forge a secure and durable peace between Israelis and Palestinians," he said.
"We do not seek a brief interlude between two wars. We do not seek a temporary respite between outbursts of terror. We seek a peace that will end the conflict between us once and for all."
Speaking next, Mr Abbas condemned attacks on Israelis and urged an end to bloodshed.
On Wednesday, an Israeli man and woman were shot and injured in the second attack in the West Bank in 24-hours.
Israeli army radio reported that the injured Israelis were travelling in a car near the Jewish settlement of Kochav Hashachar, to the east of Ramallah, when their car was overtaken by another vehicle, from which shots were fired.
The man is in a serious condition in hospital, Israeli officials have said
The militant wing of the Islamist group Hamas has claimed responsibility for both this latest incident and the shooting dead of four Israelis in the West Bank on Tuesday.
'Elephant not in the room' The BBC's Jon Donnison in the Gaza Strip says that as the peace talks get under way in Washington, Hamas seems to be sending out a message that it is not to be ignored.
The militant wing of Hamas has claimed responsibility for this week's shootings of Israelis
As a result Mr Abbas, a rival of Hamas, will be negotiating in the talks over territory that he does not even control, namely the Gaza Strip.
It is hard to see how there can be peace between Israelis and Palestinians, unless Fatah and Hamas sort out their differences first, our correspondent says.
Speaking in Washington, Mr Abbas also called for a freeze in Jewish settlement construction in the West Bank, and said it was time to end the Israeli occupation of Palestinian land that began in 1967.
"We will spare no effort and we will work diligently and tirelessly to ensure these negotiations achieve their cause," Mr Abbas said.
King Abdullah said the group needed Mr Obama's "support as a mediator, honest broker and a partner".
"If hopes are disappointed again, the price of failure will be too high for all," he said.
Settlement freeze
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End Quote Maximus Prefect commenting on BBC Have Your SayThe parties can reach an agreement on real estate and decide borders, but probably not on the real hurdle , which is the 'right of return' Palestinian claim”
Disagreement over Israeli settlement construction in the occupied West Bank has also threatened to cast a pall over the talks.
The Israelis have said they will not renew a partial freeze
on building homes for Jewish settlers when it expires towards the end of
this month, but the Palestinians say that without a freeze they will
walk away from the talks.On Thursday, US Secretary of State Hillary Clinton is to hold discussions with the Israeli and Palestinian negotiating teams.
Mr Netanyahu and Mr Abbas are to then meet for the first face-to-face talks between Israeli and Palestinian leaders since late 2008.
US officials said they wanted to at least get agreement from the two sides to meet again, possibly in the second week of September.
Another meeting between Mr Obama, Mr Abbas and Mr Netanyahu could be held during the UN General Assembly at the end of the month.