It is often that a new chance for peace in the Middle East comes when things are at their bleakest. Tensions build, talk of war grows, then the kaleidoscope is shaken and a new pattern emerges.

The flurry of initiatives now coming from Israel makes the point. Yesterday Ehud Olmert, the Prime Minister, signed a ceasefire with Hamas, under which the Palestinian militant group in Gaza today will halt the barrage of rockets fired daily into Israel, and the Israelis in turn will lift the crippling economic embargo that has kept the border crossings closed for the past six months (see page 36). Yesterday also the Israeli Government called on Lebanon to begin peace talks, offering in return to put every issue on the table. At the same time, it has emerged that Israel's indirect talks in Turkey with Syria have gone so well that there are proposals for a meeting between Mr Olmert and President Assad in Paris, the first face-to-face meeting ever to be held between the two countries' leaders.

These initiatives come at a time when Mr Olmert's domestic position is precarious. His poll ratings are the lowest ever for a prime minister. He has been accused of receiving illegal cash contributions, further damaging a political standing that has never recovered from his conduct of the 2006 Lebanon war. Tzipi Livni, his Foreign Minister, has called on him to resign and there were expectations two weeks ago that he would quit. Instead, he has hung on. And now he has decided to gamble everything on the one issue that could revive his fortunes: making peace with some or all of Israel's enemies.

Although compromised, he has little to lose, even if Israelis - and their Arab neighbours - are right to blend caution with any optimism. During the last six-month ceasefire in Gaza, residents of Sderot reported 315 missile attacks. Hamas may not be able to ensure that there are no further attacks launched by other militant groups. Egypt may not be able to seal the border, as Israel demands, to stop arms smuggling. At least, however, desperately needed supply convoys can now cross into Gaza. This will relieve Palestinian suffering and assuage global criticism of a policy of siege that clearly was not working.

The appeal to Lebanon is also unlikely to yield quick results. The country's fractured politics makes it difficult for the Government to respond, especially given the legacy of bitterness after the Israeli incursion two years ago. Fouad Siniora, the pro-Western Prime Minister, said that his country would be the last to make peace with Israel. Tantalisingly, Israel is also pursuing a prisoner swap with Hezbollah, the Iranian-backed militia that it failed to crush in 2006. If Israel can secure the return of the soldier seized in a cross-border raid in return for a Hamas militant, resolution of the disputed Shaaba Farms territory, which Israel holds and Hezbollah claims, may, in time, be easier.

The key to Lebanon, however, lies in Damascus. Here the peace initiatives look most promising, largely because President Assad is under similar political pressure, domestic and international, over Lebanon. His apparent readiness in indirect talks for a framework peace agreement, after eight years' stalling, could unlock a deal on so much else: an end to support for Hezbollah and Hamas, a distancing from Iran and the recovery of Golan. If Mr Olmert is serious, however, he must jettison his other ploy to regain support at home: encouraging expanded West Bank settlements. That policy jeopardises the hope of an ultimate and enduring deal with the Palestinians - and even of the full backing of the United States. With his back to the wall, he has reached out for peace. Mr Olmert is a compromised politician, but one who has, at last, found something positive to do with his premiership.