WASHINGTON — Seeking to broker a Mideast peace agreement that has eluded U.S. presidents for decades, the Obama administration is overseeing the first direct negotiations between Israel and the Palestinians in nearly two years.

After a day and evening in White House talks with President Barack Obama, Israeli Prime Minister Benjamin Netanyahu and Palestinian President Mahmoud Abbas sit down together Thursday for the first of what American officials hope will be a series of meetings that lead in a year’s time to an agreement on the creation of a Palestinian state.

“This moment of opportunity may not soon come again,” Obama said at the White House Wednesday night.

Obama said he was “cautiously hopeful” about the talks, which begin with dim expectations and have been marred by two shooting attacks against Israelis in as many days.

Mediated at the State Department by Secretary of State Hillary Rodham Clinton and special Mideast peace envoy George Mitchell, the two leaders’ discussions face numerous obstacles, not least renewed violence and provocations from Israelis and Palestinians opposed to the goal of an independent Palestine and secure Israel.

Gunmen from the militant Palestinian Hamas group, which opposes the talks, killed four Israeli residents of a West Bank settlement on Tuesday as Netanyahu, Abbas and the leaders of Egypt and Jordan convened in Washington. And on Wednesday, hours before the leaders were to eat dinner together at the White House, gunmen wounded two Israelis as they drove in their car in another part of the West Bank. Hamas claimed responsibility for that attack as well.

After the first attack, security forces loyal to Abbas, who heads a moderate government in the West Bank, quickly rounded up 250 Hamas members and supporters. Netanyahu said the violence would not disrupt the talks.

Before the White House dinner with Netanyahu, Abbas, Egyptian President Hosni Mubarak and Jordan’s King Abdullah II, Obama said they all had a stake in the peace efforts as leaders and fathers.

“Do we have the wisdom and the courage to walk the path of peace?” Obama asked in the packed East Room of the White House. Each of the leaders spoke of his hopes for a breakthrough, with the U.S. playing the role of peace broker, but the event was subdued, reflecting broad pessimism about chances of success after nearly two decades of failed peace talks.

Israelis “recognize that another people shares this land with us,” Netanyahu said at the White House on Wednesday. But he said any agreement must guarantee Israel’s security and could not be a repeat of Israel’s unilateral withdrawals from Gaza and Lebanon, where territory evacuated was seized by Iran-backed militants who launched further attacks on Israel.

“We left Lebanon, we got terror. We left Gaza, and we got terror once again. We want to ensure that territory we concede will not be turned into a third Iranian-sponsored terror enclave aimed at the heart of Israel,” he said.

Abbas joined Netanyahu in declaring that it was time to seize the moment. “We don’t want blood to be shed, neither that of Palestinians nor of Israelis. We want peace, we want normal life. We want to live as partners and neighbors,” he said.

But Israel, Abbas added, needs to give the Palestinians tangible signs, including freeing all Palestinian prisoners and freezing all settlement construction on land the Palestinians want for their future state.

The talks will face their first test within weeks, at the end of September, when the Israeli government’s declared slowdown in settlement construction is slated to end.

Palestinians have said a renewal of settlement construction will torpedo the talks. The Israeli government is divided over the future of the slowdown, and a decision to extend it could split Netanyahu’s hawkish coalition. Netanyahu has given no indication so far that it will continue beyond the deadline. Speaking to Clinton on Tuesday, Netanyahu said his government’s decision on a 10-month freeze that would end in September remained in effect.

Direct Israeli-Palestinian negotiations broke off nearly two years ago, in December 2008, and the Obama administration spent its first 20 months in office coaxing the two sides back to the bargaining table. Despite the success in launching the talks, gaps between the sides are wide, distrust remains after years of violence and deadlock, and expectations are low.

But American officials are hopeful they can at least get the two sides to agree to a second round of talks, likely to be held in the second week of September.

That could be followed by another meeting between Obama, Netanyahu and Abbas on the sidelines of the U.N. General Assembly near the end of the month in New York. The stated goal is to reach a final peace settlement within one year.

After listening to the Mideast leaders he convened Wednesday night, Obama pronounced himself carefully optimistic. “I am hopeful, cautiously hopeful, but hopeful,” he said.