JERUSALEM, Aug. 16 – Samuel Johnson once remarked that “when a man knows he is to be hanged in a fortnight, it concentrates his mind wonderfully.”

In that sense, recent events here – the victory of the radical Islamic movement Hamas in Gaza and Fatah ’s rapid collapse there – have focused the diplomatic mind and shaken Israel, the United States and the Sunni Arab states, like Egypt and Saudi Arabia, already nervous about a rising Iran.

In trying to gauge the seriousness of all the new talk about peace negotiations, and about where they might be headed, it seems important to keep the hangman in mind.

For Martin S. Indyk, a Clinton administration official and ambassador to Israel, there is a new “alliance of fear” that makes it possible to progress. “Only when there is a sense of urgency can things get done,” he said. “Otherwise the need for political survival trumps progress toward peace.”

After seven years of violence and terrorism, stagnation and unilateralism, the United States has finally decided to re-engage, pushing Prime Minister Ehud Olmert of Israel and President Mahmoud Abbas of the Palestinians to talk about peace. Both Mr. Olmert and Mr. Abbas may be weak, but both are also desperate for accomplishment. And the landscape is very different than it was seven years ago.

After trying to undermine Hamas and seeing it conquer Gaza, the United States and Israel act as if they now have Hamas exactly where they want it, as if the fruits of defeat are sweeter than those of victory. Embracing a non-Hamas government in the West Bank, one run by an independent economist, Salam Fayyad, appointed by Mr. Abbas of Fatah, they are trying to make the West Bank a model.

The fact that Hamas won a legislative majority, that Mr. Fayyad has no mandate, that there is no functioning legislature and no democratic oversight are all the complications of necessity, Israeli officials and American diplomats argue.

For what is at stake, all now seem to understand, is the future of the two-state solution, of a negotiated territorial compromise between Israelis and Palestinians over the same slice of earth.

But hanging over that issue, of course, is the fallout from Iraq and the larger regional challenge of a Shiite Iran pursuing nuclear weapons and sponsoring those most opposed to a permanent deal – Hamas and Islamic Jihad in the territories, Hezbollah in southern Lebanon.

The Bush administration finally seems to understand, one American official said, that there is no sustainable status quo. Even more, Condoleezza Rice, the secretary of state, seems now to understand, as Shlomo Ben-Ami, a former Israeli foreign minister put it, “If there was an Archimedean point to the Middle East problem, it was to be found in the Palestinian issue, not the ‘war on terror,’ Iraq or the need for Arab democracy.”

But unlike President Bill Clinton, whose team did not take or have the time to get Arab support for Yasir Arafat at Camp David, President Bush appears to have Saudi Arabia, which is worried about Iran, on board, providing an Arab umbrella over Mr. Abbas and Mr. Fayyad.

But to do what, exactly? Mr. Indyk, at the Brookings Institution and thinking about the lessons of Camp David, warns against hubris. “If Rice goes for final status she’ll drive it into the ground,” he said. Israel does not have enough confidence in Mr. Abbas or a divided Palestinian polity to pull out of large sections of the West Bank, fearing Gaza-like chaos that could rain rockets on Ben Gurion airport.

What is needed, Mr. Indyk said, is a parallel and simultaneous process of Palestinian state building and negotiation over a peace deal, so that the rest of Mr. Bush’s term is not wasted. Here, if possible, the former British prime minister, Tony Blair, and Ms. Rice can work in tandem, with Mr. Blair helping the Palestinians finally build the institutions of a state while Ms. Rice pushes both sides to agree on what peace would look like.

Ms. Rice speaks carefully about negotiations on the principles of a final settlement – not the final settlement itself, which will be carried out over many years. Ideally, some of those principles can be put into a text – not a peace treaty – that can be endorsed by an international meeting for which Ms. Rice will be host, probably in November.

An example, officials say, could be an agreement that Israel and the Palestinians accept 1967 boundaries with modifications and land swaps that give the new Palestinian state Gaza and some percentage of the current area of the occupied West Bank – maybe 97 percent, as Mr. Clinton proposed, or perhaps 100 percent, as the Arab League wants, and as the Israeli president, Shimon Peres, recently suggested.

The parties could negotiate the details of the swaps and how to carry them out later, but the principle would be established and embraced by the West and the Arab League, making it harder for Hamas to reject. But the harder issues have always been the emotional and religious ones: Jerusalem, the Temple Mount, known to Muslims as Haram al-Sharif, and refugees.

Among the Israelis and Palestinians, parties and factions are already fighting about how to approach the new American initiative. It comes late in Mr. Bush’s term. But what may make it work is its essential modesty, given Ms. Rice’s apparent understanding that a full settlement is out of reach.