There is also considerable diplomatic weight behind the goal of having two viable states living in peace side by side. In December, with the Obama administration’s tacit support, the United Nations condemned Israeli settlements on occupied land as obstacles to the two-state solution.

But lately the chances of achieving it have been dimming. Many Israelis and Palestinians have begun to doubt whether it is possible or even desirable.

Many Israelis argue that the Palestinians in the West Bank and Gaza are too divided among themselves to ever be able to permanently accept two states. Some in the Israeli right advocate annexing all or part of the West Bank, and some rightists warned Mr. Netanyahu not to raise the possibility of two states in his meeting with Mr. Trump.

At the same time, many Palestinians say the line has already been crossed — that Israeli settlements have already eliminated the possibility of creating a contiguous Palestinian state. Instead, they advocate a single state encompassing both Israel and the occupied territories — a secular state where Palestinians and Israelis would live together with equal rights.

At a news conference on Wednesday in the West Bank, Mr. Erekat said the only alternative to what he called Mr. Netanyahu’s “apartheid” vision was “one single secular and democratic state with equal rights for everyone, Christians, Muslims and Jews, on all of historic Palestine.”

That is opposed by many Israelis, who want Israel to remain a Jewish state.

Some Israelis say that the deep divisions between the Palestinian factions that control the West Bank and Gaza are another reason that it will be impossible to reach an agreement on two states. The Fatah faction in the West Bank has tried to cooperate with the Israeli authorities on some levels, while Hamas, the group that has controlled Gaza since 2007, is more actively hostile to Israel.

Hazim Kassim, a spokesman for Hamas, said on Wednesday, “What Trump said is new, but whatever he says, we in Hamas still believe that resistance is the only way to liberate our lands from the Israeli occupation.

“It is now clear that the U.S. has provided a cover for aggression, occupation and the confiscation of Palestinian land,” he continued. “The U.S. is never serious when it comes to Palestinians’ human rights.”