“I believe the conditions have been created to permit us and the Palestinians to reach an historic breakthrough, a breakthrough that will lead us to security and peace,” the Israeli Prime Minister told business leaders in Jerusalem in a surprisingly upbeat speech.

If the Palestinian leadership moved to “end terrorism, incitement and violence”, he said, Israel would be ready to resume talks on the “road map” peace plan that envisages the creation of a Palestinian state.

Amid further signs of a thaw in Palestinian-Israeli relations, Ahmed Qureia, the Palestinian Prime Minister, issued a decree yesterday banning civilians from carrying weapons and hinted at the appointment as Interior Minister of the tough Nasser Yousef. Mr Yousef had distinguished himself in a previous clampdown on hardline factions.

Even before the weapons ban was announced, Mr Sharon voiced approval of the new Palestinian leadership, singling out for praise Mahmoud Abbas, the President of the Palestinian Authority who is also known as Abu Mazen.

“There is no doubt Abu Mazen has started to work,” Mr Sharon told Yedioth Ahronoth newspaper. “I am very satisfied with what I am hearing is happening on the Palestinian side and I am very interested in advancing processes with him.

“I intend to be accommodating towards Abu Mazen, while at the same time remaining vigilant and assessing the situation on their side.”

Echoing Mr Sharon’s optimism, Palestinian sources said that deals were already being struck. Mohammad Dahlan, a senior Palestinian security figure and a key adviser to Mr Abbas, said that Israel had agreed in principle to pull back its troops from West Bank cities and hand control to Palestinian security forces.

Details of the deal had not been finalised, Mr Dahlan conceded but he said that Israel had given tacit backing to the withdrawal.

The security chief, who is due to meet Shaul Mofaz, the Israeli Defence Minister, next week, said that the pullout from West Bank cities would be in line with earlier agreements reached during Mr Abbas’s brief four-month tenure as Prime Minister in 2003.

“Israel has agreed in principle to renew the understandings that were reached when Mr Abbas was Prime Minister,” Mr Dahlan said. He also said that Israel had indicated that it would stop pursuing wanted militants and halt targeted assassinations.

The unusually friendly exchanges between the two opposing sides followed a flurry of diplomatic activity as Dov Weisglass, a senior adviser to Mr Sharon, met Saeb Erekat, the Palestinians’ chief negotiator. Mr Abbas also held talks with William Burns, the US envoy, who said that America was “very encouraged” by Palestinian steps towards a “restoration of law and order”.

But amid all the positive noises, Mark Regev, an Israeli Foreign Ministry spokesman, struck a cautious note, denying that an agreement to release hundreds of Palestinian prisoners had been reached.

Yesterday’s local elections in Gaza also dampened the euphoria. In a sign of continued support for hard- liners, exit polls showed that the extremist Hamas movement was heading for victory in three of four large towns in the Gaza Strip, beating Mr Abbas’s Fatah into second place.

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