It must be assumed that the discussion at the somewhat reluctantly and hastily arranged meeting in Washington last night between Barack Obama, the US president, and Benjamin Netanyahu, the Israeli prime minister, would have focused almost exclusively on the future of the Palestinian-Israeli peace process.

Certainly, Palestinian leaders and officials are publicly declaring that future is at risk. In Hebron, on Sunday, Mahmoud Abbas, the head of the Palestine Liberation Organisation and Palestinian Authority (PA), said there was “no possibility of establishing a Palestinian state while settlements continue”, and urged Israelis to ponder what they really wanted, “if they want peace”.

He reiterated his position that there could be no resumption of negotiations with Israel while the settlement construction continued. A freeze on such construction is one of the obligations on Israel under the 2003 Quartet-sponsored road map. It is also the main reason Mr Abbas cited last Thursday for his desire not to seek re-election in any new Palestinian elections.

The Quartet is composed of the United States, Russia, the European Union and the United Nations.

Saeb Erekat, the PLO’s chief negotiator, last week warned that it would not rule out any option, including abandoning the two-state solution and dismantling the PA to pursue a one-state solution, in which Palestinians would push for equal rights alongside Jews on all the territory of historic Palestine. He, too, cited Israeli settlement construction as the main obstacle to the peace process.

The Israeli media, meanwhile, have been rife with rumours that Salam Fayyad, the PA prime minister, has struck a secret agreement with the US to unilaterally declare an independent Palestinian state. PA officials have rejected those reports, but the idea of unilaterally declaring statehood is not a new one and was only narrowly rejected by Yasser Arafat after negotiations collapsed at Camp David in 2000.

Both the US and Israel have remained muted in their reactions to these statements. In Israel, Mr Abbas’s stated desire not to run for re-election is seen by many as simply a political manoeuvre.

“Israelis see it as a transparent ploy to put pressure on Israel,” said Gerald Steinberg, a professor of political science at Bar Ilan University in Tel Aviv. “The Israeli inclination is to see it as primarily a Palestinian issue.”

Mr Steinberg rejected talk of a one-state solution as a “very unlikely process” that “wouldn’t make any difference as far as Israel was concerned”. He said statements by Palestinian officials that the peace process was at risk were “an empty threat”.

“Israelis don’t see the peace process as endangered because it never really started again.”

Nevertheless, it is hard to avoid the conclusion that the Palestinian-Israeli peace process may have run its course.

The Palestinian negotiating position has been constant since the Oslo process, and Mr Abbas has in recent days reiterated that position. A two-state solution for the Palestinian leadership means an independent Palestinian state created on the 1967 borders, with minor adjustments and equal territorial swaps. East Jerusalem should become the capital of a Palestinian state while a “formula” will be agreed between the parties for the return of Palestinian refugees. This among Palestinian politicians is known as the “historic compromise”, a compromise because it gives up Palestinian claims to 78 per cent of historic Palestine.

Even Hamas, the Islamist movement that is implacably opposed to any peace process with Israel, has declared that under such a scenario it would enter into a generation-long ceasefire with Israel and leave it to future generations to decide whether this should be the long-term solution.

Israelis, however, reject this approach. As far as successive Israeli governments have been concerned, the peace process meant negotiating over what territory of the West Bank and Gaza Palestinians might exercise self-rule over.

Ariel Sharon, the stricken former prime minister, was the first sitting Israeli government leader to talk officially of Palestinian statehood, but only over a limited amount of occupied territory.

Mr Netanyahu has reluctantly endorsed the idea of Palestinian statehood and only in the most lukewarm of terms. Meanwhile, any talk of Jerusalem, unilaterally annexed by Israel in 1967, is an Israeli “concession” in itself while a return of refugees to Israel itself would at most be symbolic.

Throw into the mix Israeli settlements, illegal under international law, which continue to grow, taking more of the territory that Palestinians envisage for their state, and with it any incentive for Palestinian leaders to continue negotiating. There are now half a million Jewish settlers residing in occupied territory. Nine of them sit in the Israeli cabinet, and the current Israeli coalition is committed to the settlement project.

With positions this far apart, a negotiations process, even if it could get off the ground, would seem moribund from the outset. That may be bearable for Israelis, at least in the absence of a third intifada, but it is not for Palestinians, who continue to live under military occupation, with the attendant restrictions on their movement and economy as well as recourse to the law.

In this context, Palestinians largely feel the options have run out.

“We are stuck, the Israelis are stuck and so are the Americans,” said Mustafa Abu Sway, a political scientist at Al Quds University.

“Practically, people may be pushed to a one-state solution even if it is not their declared aim,” Mr Abu Sway said. “There is no progress in [Palestinian-Israeli] talks, there is no willingness on the part of Netanyahu to consider the 1967 borders as the borders, settlements continue to expand. On the ground, Israel is pushing for a one-state solution without knowing it, by making a two-state solution impossible.”