“I said, ‘Look, my son, we are looking for two-state solution and this is the only one.’ He said, ‘Oh, my father, where is your state? I wander everywhere and I see blocks everywhere, I see houses everywhere,' ” the elder Mr. Abbas, 78, recalled. “I say, ‘Please, my son, this is our position, we will not go for one state.’ He says, ‘This is your right to say this, and this is my right to say that.’ Because he is desperate. He doesn’t find any sign for the future that we will get a two-state solution, because on the ground he doesn’t see any different.”

Such intergenerational arguments have become commonplace in the salons of Palestinian civil society and at kitchen tables across the West Bank as the children and grandchildren of the founders of the Palestinian national movement increasingly question its goals and tactics.

In a December poll by the Palestinian Center for Policy and Survey Research, 65 percent of people over 50 said they supported the two-state solution, compared with 47 percent of those 18 to 34. Khalil Shikaki, the center’s director, said that about a third of all Palestinians expressed interest in the one-state alternative, but that its backing among those under 45 is more solid and “cannot be satisfied by a two-state solution.”

“Just ask my son,” Mr. Shikaki, 60, wrote in an email. “He will tell you that my generation has failed and should exit the stage and take its mainstream paradigm, the two-state solution, along with it.

“The views of my generation were formed during the heyday of the Palestinian national movement; his views were formed during the failed years of Oslo, the days of perceived Palestinian Authority corruption and tyranny, the Internet and social media,” Mr. Shikaki added, referring to the 1990s Oslo accords, which laid the two-state groundwork. “We are pragmatic; he is idealistic. We demand independence and sovereignty; he demands equal rights.”