JERUSALEM — From across the ocean and across the Green Line, they came on Friday to the mountaintop sanctuary of Mount Herzl to bid farewell to Shimon Peres, marking what one called the “end of the era of giants.” But the question of the moment was whether it was a funeral for a man or for his dream.

Twenty-three years after Mr. Peres helped negotiate the Oslo Accordsheralding peace between Israelis and Palestinians, President Obamaand other leaders from around the world paid homage to his tenacious search for reconciliation. And yet the memorial service made clear how elusive that idea has actually become in this part of the world.

The funeral brought together Prime Minister Benjamin Netanyahu ofIsrael and President Mahmoud Abbas of the Palestinian Authority, something no mediator has been able to do in recent years, and the men shook hands and exchanged pleasantries. But the encounter went no further, and the momentary pause in their war of words seemed unlikely to last beyond the interment.

In his eulogy, Mr. Netanyahu welcomed by name many of the foreign figures in attendance without mentioning Mr. Abbas. It was left to Mr. Obama to acknowledge the Palestinian leader, saying that his “presence here is a gesture and a reminder of the unfinished business of peace.”

For his part, Mr. Abbas, in a move perceived by some analysts as a jab at Mr. Netanyahu’s government, brought along an adviser, Mohammed al-Madani, who was barred by Israel last summer for “subversive” activities. No ruler, president or prime minister of an Arab country came, although Egypt sent its foreign minister and others sent lower-ranking officials.

Amos Oz, the famed Israeli author and a friend of Mr. Peres’s, gave voice in his eulogy to what others were thinking, wondering about the fate of peace in a new era. With Israelis and Palestinians sharing a small piece of the world, he said, the only solution is the creation of a Palestinian state that Mr. Peres supported.

“In their heart of hearts, all sides know this simple truth,” Mr. Oz said as Mr. Netanyahu and Mr. Abbas listened. “But where are the leaders with the courage to come forward to make it come to pass? Where are the heirs to Shimon Peres?”

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Mr. Obama, who has been pressing the two sides to rejuvenate a peace process, made a similar point less directly. “Shimon never saw his dream of peace fulfilled,” he said. And so, he added, “Now this work is in the hands of Israel’s next generation, in the hands of Israel’s next generation and its friends.”

The funeral drew delegations from 75 countries and such figures as former President Bill Clinton, President François Hollande of France, Prime Minister Justin Trudeau of Canada, President Enrique Peña Nieto of Mexico and King Felipe VI of Spain.

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About 4,000 mourners gathered underneath a tent on a warm, cloudless day at the national cemetery overlooking Jerusalem. Security was tight.

Mr. Peres, who died this week at 93, embodied the history of the Israeli state. A protégé of David Ben-Gurion, the founding prime minister, he had a role in most of Israel’s major events from its independence in 1948. He served as prime minister, foreign minister, defense minister and president.

A longtime security hawk, he helped build the nation’s military and was instrumental in developing its nuclear program. Critics, especially Palestinians, castigate him for promoting the construction of settlements in territories seized in the Arab-Israeli war of 1967 and for launching military operations that led to civilian deaths.

He was remembered on Friday mainly for his pursuit of peace, which resulted in the Nobel Peace Prize he shared in 1994 with Prime Minister Yitzhak Rabin and Yasir Arafat, the leader of the Palestine Liberation Organization.

But the peace process ultimately stalled, and today the region looks little like the peace once envisioned, amid continuing occupation, settlement construction, terrorism and incitement.

Mr. Netanyahu and Mr. Abbas both say they are willing to negotiate, and each blames the other for resisting. Mr. Obama tried twice to restart talks, in vain, and is contemplating laying out his own proposed parameters for peace before leaving office in January.

Mr. Obama, who flew overnight to attend the funeral and finished writing his eulogy only as Air Force One landed, offered an especially personal tribute to Mr. Peres. This was only the second time in nearly eight years in office that he had traveled overseas for the funeral of a foreign leader, after Nelson Mandela, and indeed, he compared Mr. Peres to the South African leader.

Mr. Obama tried to explain the unlikely friendship that developed between an African-American from Hawaii and a child of the shtetl who grew up to lead Israel. “We shared a love of words and books and history and, perhaps like most politicians, we shared, too, a great joy in hearing ourselves talk,” he said. “But beyond that, I think our friendship was rooted in the fact that I could somehow see myself in his story and maybe he could see himself in mine.”

Echoing Mr. Clinton, who in 1995 memorably bid farewell to the assassinated Mr. Rabin by saying, “Shalom, chaver” (“Farewell, friend”), Mr. Obama ended his eulogy for Mr. Peres by saying, “Todah rabah, chaver yakar” (“thank you, dear friend”).

Mr. Netanyahu was emotional, too, choking up as he recalled the death of his brother Yoni, a commando killed in a hostage rescue mission in Entebbe, Uganda, in 1976, and the “deeply stirring” eulogy that Mr. Peres, then the defense minister, delivered.

He ousted Mr. Peres as prime minister in 1996, but Mr. Netanyahu said they later became close friends and he spoke lovingly of their arguments over the best way to pursue peace for Israel.

“We went back and forth for hours, flinging arguments at one another,” he said. “He came from the left, I came from the right. I came from the right, and he came back from the left. And in the end, like two worn-out prizefighters, we put down our gloves. I saw in his eyes, and I think he saw in mine, that our principles stemmed from deep-seated beliefs and a commitment to the cause — ensuring Israel’s future.”

It is Mr. Netanyahu’s theory of the case, that peace will come only through security, not concessions, that has resonance in today’s Israel. Indeed, the failure of the Oslo agreement to lead to an enduring peace has soured many here on it. Almost none of the eulogies on Friday used the word Oslo. Even the biography of Mr. Peres read to the crowd at the beginning of the funeral omitted the name most associated with his long career.

The idea of a negotiated resolution seems so out of reach that one eulogist after another used the word “naïve” to describe the impression Mr. Peres left, even as they argued that it was a misunderstanding of his idealism.

The obstacles to progress were evident on Friday. Mr. Netanyahu and Mr. Abbas, who have not formally met in six years, shook hands before the service, as they did last year on the sidelines of a climate conference in Paris.

“Long time,” Mr. Abbas said as he greeted Mr. Netanyahu and his wife, Sara. “Long time.”

“Thank you for coming,” Mr. Netanyahu said. “I appreciate it.”

But both came under fire just for that. Mr. Abbas’s decision to come to a cemetery named for the founder of modern Zionism, Theodor Herzl, angered many Palestinians, who criticized him for honoring an enemy. In Gaza, one militant faction said in a statement that “every drop of blood from Arab and Muslim martyrs will curse Abbas.”

It was a delicate issue on the other side, too, as Israeli officials debated overnight whether to seat Mr. Abbas in the front row. Ultimately they did, but he had no speaking role. Afterward, Naftali Bennett, a hard-line member of Mr. Netanyahu’s cabinet, criticized the prime minister for shaking hands with Mr. Abbas, who “is encouraging the murder of Israelis,” as he wrote on Facebook, adding, “Let him stop funerals before attending funerals.”

The enduring impasse even tripped up the Americans. A White House transcript of Mr. Obama’s eulogy had to be quickly corrected after it initially was sent out with “Jerusalem, Israel” as the location of the remarks, in violation of a longstanding United States policy that refuses to recognize any country’s sovereignty over the city until a final peace agreement resolves the issue. A second copy of the president’s remarks listed the location only as “Jerusalem.”

As for Mr. Peres, for a man who made a legacy of bridging divides, there was one final act of reconciliation: He was buried between two onetime rivals, Mr. Rabin and another former prime minister, Yitzhak Shamir.