President Obama vowed Wednesday to press ahead with peace talks in Washington just one day after Palestinian gunmen killed four Israelis -- an act of violence that Obama described as "senseless slaughter" designed to undermine negotiations. 

But Obama told Israeli and Palestinian leaders they faced a fleeting chance to settle deep differences after decades of hostility.

"I am hopeful, cautiously hopeful, but hopeful," Obama said with the leaders of Jordan, Egypt, Israel and the Palestinians beside him in the crowded East Room of the White House. Earlier Obama had met with each individually, and they gathered afterward for dinner.

In turn, each of the leaders said they were committed to talks, but with qualifications. And they spoke of hopes for a breakthrough within the one-year timeframe prescribed by Obama.

Israeli Prime Minister Benjamin Netanyahu said his nation desires a lasting peace, not an interlude between wars. He called Palestinian President Mahmoud Abbas "my partner in peace," and said, "Everybody loses if there is no peace."

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Abbas urged Israel to freeze settlement construction in areas the Palestinians want as part of their new state, and to end its blockade of Gaza, which is controlled by the militant Hamas movement. The settlements issue is a central obstacle to achieving a permanent peace.

"We will spare no effort and we will work diligently and tirelessly to ensure these negotiations achieve their cause," Abbas said, as translated into English.

Earlier, Obama had sought to temper expectations, noting that it had taken his administration this long just to get the two sides back to the bargaining table.

"The hard work is only beginning," Obama said, with Secretary of State Hillary Clinton and special Middle East peace envoy George Mitchell at his side. "Neither success nor failure is inevitable. But this much we know: If we do not make the attempt, then failure is guaranteed. If both sides do not commit to these talks in earnest, then long-standing conflict will only continue to fester and consume another generation, and this we simply cannot allow."

The new round of ambitious Middle East peace talks came as tensions flared over the latest attack that Hamas claimed responsibility for.

"This is not going to stop us," Obama said earlier Wednesday. "We are going to remain stalwart." 

Standing beside Obama, Netanyahu condemned the shooting but described an opening one-on-one session held with the president as "open, productive, serious in the quest for peace." 

While top officials in the U.S. and Israeli administrations vowed that negotiations would press ahead, Netanyahu was already starting to hear calls for vengeance back home. 

"There is an army, which must be used," Rabbi Dov Lior said at the funeral for the murdered Israelis, according to Haaretz. "The mistake is to think that an agreement can be reached with these terrorists. Every Jew wants peace, but these evildoers want to destroy us." 

Israeli settlers in the West Bank threatened to break a construction freeze and at least one member of Israel's Knesset, Uri Ariel, called for Netanyahu to "freeze talks" because "the most violent periods take place when there is a political process." 

Tensions flared in Israel as Obama entered several rounds of one-on-one talks with the leaders involved in the broader peace talks, set to begin Thursday. Obama met with Netanyahu and moved on to sit down with Palestinian Prime Minister Mahmoud Abbas, Jordanian King Abdullah and Egyptian President Hosni Mubarak

Netanyahu said Wednesday that his government would "find the murderers" and "punish their dispatchers" while negotiations proceed. 

Clinton said such "savage brutality" cannot be tolerated in the face of the peace process. 

"The forces of terror and destruction cannot be allowed to continue. It is one of the reasons why the prime minister is here today: to engage in direct negotiations with those Palestinians who themselves have rejected a path of violence in favor of a path of peace," Clinton said. "We have to not only stand against the kind of horrific murders we saw today on behalf of the four who were lost and, as the prime minister said, the seven orphans who have been brutally deprived of their parents, but on behalf of all people -- Israelis, Palestinians, everyone who knows that there is no answer when violence begets violence." 

Abbas, too, was trying to show his commitment to cracking down on the violence, as his government reportedly arrested more than 250 members of Hamas in the wake of the shooting. 

Two men and two women were killed in their car in the attack near Hebron in the West Bank. It was a reminder of the problems Hamas can cause for the peace process -- though the faction is not at the table in Washington, it controls the Gaza Strip

The U.S. government has tried to temper the rhetoric on both sides with Obama aiming for a peace agreement within one year -- a lofty goal as he embarks on a diplomatic mission so many U.S. presidents have failed to complete. 

The Associated Press contributed to this report.