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 Accords heralding peace between Israelis and Palestinians, President Obama and 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 of Israel 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.