End of the two-state solution? What Israel, Palestinians would be giving up.

President Trump said he was not insisting on a two-state solution for Middle East peace. Palestinians and Israelis view the one-state option very differently.

When President Trump dropped the longstanding American insistence on the creation of a Palestinian state alongside Israel, he veered away from the two-state premise that has been at the core of Middle East peace efforts for decades.

The idea of dividing the land shared by Israelis and Palestinians goes back to 1947. That's when the United Nations voted to partition British-ruled Palestine, creating a Jewish and an Arab state, a plan the Jews accepted and the Arab states did not.

For more modern proponents of the two-state solution to the Israeli-Palestinian conflict, the model enshrined the principle of trading “land for peace.” It promised two essential ingredients that sought to satisfy the basic needs of the two peoples: political self-determination for the Palestinians in their own independent state, and recognized borders for Israel that would be accepted by its Arab neighbors.

The goal of an independent Palestinian state in the West Bank and Gaza Strip became American policy after the 1993 Oslo accords between Israel and the Palestine Liberation Organization.

The two-state objective was first enunciated by President Bill Clinton in 2001, adopted as official policy by his successor, George W. Bush, and was a cornerstone of the Obama administration's peace efforts.

Mr. Trump upended all that on Wednesday when he said he was "looking at two-state and one-state" options, and would be "very happy with the one that both parties like." He spoke before meeting with Israeli Prime Minister Benjamin Netanyahu, who pointedly avoided mention of the two-state solution.

As repeated efforts to broker a two-state deal have foundered, some Israelis and Palestinians have spoken of an irreversible reality on the ground in which, they argue, Jewish settlements scattered across the West Bank and a half century of Israeli control have  doomed a territorial compromise.

But a one-state reality carries its own perils, critics of the idea say.

"A one-state solution is the end of Zionism," says Shlomo Avineri, a professor of political science at the Hebrew University of Jerusalem. "Zionism is about a Jewish national state, not a binational state."

An Israeli state that includes the Palestinians could deny them equal rights and lose its Jewish majority to a faster-growing Arab population, according to the critics.

"Only the two-state solution will preserve Israel as both democratic and Jewish," says Avi Buskila, head of Peace Now, an Israeli group that opposes Jewish settlement in the West Bank and backs a Palestinian state.

In a single Israeli state "either the Palestinians would not have equal rights and it would be an apartheid state, or they could have equality and become the majority, meaning it would no longer be Jewish."

Saeb Erekat, the chief Palestinian negotiator, says jettisoning the two-state solution would be a "disaster for both Palestinians and Israelis."

The only alternative is "one democratic state of Jews, Christians, and Muslims living in one state as equal citizens in one country," Mr. Erekat says. "Netanyahu's scheme of trying to impose one state with two systems, an apartheid regime, is not doable in the 21st century."

A "secular democratic state" in the entire area between the Jordan River and the Mediterranean Sea was a longtime goal of the PLO before it accepted a state in the West Bank and Gaza Strip and recognized Israel.

"Our understanding of one state would be a democracy with equal rights in which I could become president or prime minister of Israel," says Mustafa Barghouti, a prominent Palestinian legislator and activist. "If this state is truly a democracy it cannot be Jewish, it will be a joint state. I would love to go back to one democratic state in which Palestinians can live in [the Israeli cities] of Jaffa and Haifa. But a one-state solution for Netanyahu would be nothing but consolidation of a full apartheid system in all the area of Palestine."

In his remarks before meeting Trump, Mr. Netanyahu said Israel would have to maintain security control over the entire West Bank in any future peace deal, and he asserted that he would not agree to a Palestinian "terrorist" state on Israel's borders.

Israeli rightists welcomed what they saw as Trump's step away from a two-state solution.

Justice Minister Ayelet Shaked, a member of the staunchly pro-settlement Jewish Home party, told Israel Radio Thursday that the president's position was "a very significant and important change from the entrenched thinking of the last 20 years."

"You can see that President Trump is open to new ideas," she added, asserting that her party would press for annexation to Israel of some 60 percent of the West Bank that remains under full Israeli control, while granting the Palestinians "autonomy" in other areas controlled by the Palestinian Authority.

Netanyahu and Trump spoke about efforts to involve Arab states in a regional effort to broker a peace deal, countries that Netanyahu has said share with Israel a common concern about growing Iranian influence in the Middle East.

Professor Avineri calls that vision unrealistic, arguing that no Arab détente with Israel can be expected before an agreement with the Palestinians. "This was really a flabbergasting example of Trump's ignorance about the Middle East," he says.