A day after Israeli and Palestinian leaders committed themselves to negotiating a peace treaty, the Bush administration sought Wednesday to give practical and symbolic impetus to their reinvigorated peace process.

President Bush on Wednesday with the Palestinian Authority leader, Mahmoud Abbas, left, and Prime Minister Ehud Olmert of Israel.

Secretary of State Condoleezza Rice appointed a retired NATO commander, Gen. James L. Jones, to oversee security, an issue that remains at the heart of the political differences between the Israelis and Palestinians.

At the White House, President Bush met for the third consecutive day with Prime Minister Ehud Olmert of Israel and Mahmoud Abbas, the president of the Palestinian Authority, though in separate meetings.

After the diplomatic wrangling that culminated with Tuesday’s meeting at the United States Naval Academy, in Annapolis, Md., the meetings on Wednesday focused on bilateral relations and the next steps in the peace process, according to Mr. Bush’s press secretary, Dana M. Perino.

The three leaders, with their aides, also met for 20 minutes informally in the Oval Office and then appeared in the Rose Garden as Mr. Bush offered a short statement that seemed strikingly subdued after the emotional appeals of Annapolis.

“Yesterday was an important day, and it was a hopeful beginning,” Mr. Bush said, bracketed by the two leaders, their hands behind their backs. “No matter how important yesterday was, it’s not nearly as important as tomorrow and the days beyond.”

Neither Mr. Olmert nor Mr. Abbas spoke at the White House.

The Israeli prime minister later met with journalists and voiced reservations even as he said he was committed to trying to reach an agreement by the end of 2008. He conditioned any deal on the Palestinians’ fulfillment of the terms of the “road map,” an agreement from 2003 that linked negotiations to steps from both sides and that both sides have complained was broken from the start.

“We will do all we can to try to reach an agreement as soon as possible, and we can do it,” Mr. Olmert said. “It doesn’t mean you can implement it. We can’t implement an agreement unless and until you have the terms of the road map fulfilled.”

Ms. Rice’s appointment of General Jones appeared intended to signal a reinvigoration of the American involvement, something that the administration’s critics have said was sorely lacking in Mr. Bush’s first seven years in office.

General Jones, a French-speaking Marine officer seasoned in diplomacy, stepped down in December as NATO’s supreme commander. Since then he has led the energy institute at the United States Chamber of Commerce. He also led a Congressional commission that reported in September on the shortcomings of Iraq’s national police.

Ms. Rice said he would oversee “the full range of security issues” for the Israelis and Palestinians, as well as security cooperation with neighboring countries and American efforts to provide assistance to the Palestinian Authority.

“Any lasting peace must be built on solid foundations of security,” she said. “Israelis must be confident that a Palestinian state will increase their security, not detract from it. Palestinians must be capable of standing on their own and policing their territory, and countries in the region must be invested in the success of this state-building effort, for their own security depends on it, too.”

One of the provisions of the agreement reached Tuesday made the United States the arbiter of the commitments under the 2003 road map. Mr. Bush promised in 2003 that he would “ride herd” on the participants to ensure that the agreements were kept — only to see the Palestinian territories descend again into violence and Israeli settlement growth continue.

Officials and outside experts broadly agreed that the prospects for achieving the peace promised at Annapolis would depend on the willingness of the Bush administration to press the two sides to compromise.

Rafi Dajani, executive director of American Task Force on Palestine, a group in Washington that advocates a negotiated settlement and Palestinian state, said all the previous efforts had stalemated because of the failure to police their initial agreements.

“Previous attempts to implement the road map foundered on vastly different interpretations of, No. 1, what their road map obligations meant and, No. 2, when they were fulfilled,” he said. “There was nobody there as the arbiter.”

Appearing at Johns Hopkins University, though, Mr. Bush’s national security adviser, Stephen J. Hadley, said the Annapolis agreement was possible because the United States was not imposing terms of a peace treaty on the two sides.

“The president will not force a resolution of differences,” Mr. Hadley said, according to a transcript, “nor impose a peace plan with his name on it.”

More Violence on West Bank

HEBRON, West Bank, Nov. 28 — Palestinian Authority security forces loyal to President Mahmoud Abbas opened fire Wednesday to disperse a funeral procession that had turned into a pro-Islamic rally. It was the second day of violence in this usually staid West Bank city.

At least 24 protesters were hospitalized, some with gunshot or shrapnel wounds and others with injuries from police batons, hospital officials and witnesses said.

Muhammad Abu Atwan, a spokesman for the Palestinian Authority security forces in Hebron, said nine police officers had been injured in clashes with stone-throwing protesters. He denied that any civilians had been hurt by police bullets.

The funeral was for Hisham al-Baradei, a local man in his 30s who was killed Tuesday after the police opened fire to end a protest organized by Hizb ut-Tahrir, the Party of Liberation. That demonstration was against the peace conference in Annapolis.

Palestinian security officials have denied that Mr. Baradei, who was shot in the chest, was killed by police bullets.