Some wars look as if they should be easy to stop. The Israeli-Palestinian fighting over the last year or so in Gaza is an example: neither side had any coherent military objective, the Israelis had already withdrawn their settlements, and each claimed that its attacks were purely in retaliation for those of its opponents.

The difficulty with such situations is getting someone to make the first move. But last weekend, quite unexpectedly, it happened. The Palestinian militant groups offered to stop rocket attacks on Israel in return for an end to Israeli military operations in Gaza, and Israel decided to take them at their word.

So far the ceasefire seems to be holding, to the immense relief of residents in the area. But its long-term prospects are slim unless it can be made a part of a more general settlement. The few rockets that have been fired this week have come from the Al-Aqsa Martyrs Brigades, which claims to be retaliating for Israeli attacks in the West Bank.

Hence the importance of a speech on Monday by Israeli prime minister Ehud Olmert in which he appeared to open the door to wider peace negotiations with the Palestinians.

The Australian’s Martin Chulov yesterday called it “the most important by an Israeli leader since former prime minister Ariel Sharon addressed the UN General Assembly 14 months ago”.

Olmert signalled an end to his previous unilateralism, saying “I hold out my hand in peace to our Palestinian neighbours” and offering the prospect of major concessions leading to the ultimate establishment of a viable Palestinian state.

Some Palestinian representatives have dismissed Olmert’s words. But a sign of their importance is the furious reaction they have aroused on the Israeli right, with hard-line Zionists describing the speech as defeatist and a victory for terrorism.

Israel is divided between those who are convinced that they are fighting World War III, in which any negotiation is tantamount to surrender, and those who realise that the military option is not working and somehow the parties are going to have to start talking to each other.

As an editorial in Le Monde put it on Tuesday, the Gaza ceasefire “has shown the Israeli government that what cannot be obtained by force cannot be obtained by still more force.”