Mr Sharon indicated a willingness to withdraw from the West Bank and Gaza - unusually for him describing Israel’s military presence in the Palestinian territories as an "occupation".
"I think that the idea of keeping 3.5 million Palestinians under occupation is the worst thing for Israel, for the Palestinians and also for the Israeli economy," the website of Israeli daily Maariv quoted him as saying.
Mr Sharon and his Palestinian counterpart Mahmoud Abbas, better known as Abu Mazen, are expected to meet on Wednesday in Jerusalem, Israeli officials said.
It would be their second meeting since Abu Mazen took office on 30 April.
Mr Sharon faced fierce criticism from within his own Likud party on Monday - with 11 ministers and deputies making blistering attacks on the international peace initiative known as the roadmap, Israeli army radio reported.
The Israeli prime minister's comments came as US President George W Bush is considering holding a summit with the Israeli and Palestinian prime ministers in Jordan next week, Israel has said.
Israeli Foreign Minister Silvan Shalom said the talks would focus on implementation of the roadmap.
Violence continues
Some of Mr Sharon's critics have expressed doubt over his comments, saying that his newfound willingness to compromise is merely a political manoeuvre as he does not expect it to be put to the test.
Meanwhile, violence has continued with an 11-year-old Palestinian boy shot dead in the West Bank during a confrontation between stone-throwing youths and Israeli soldiers, witnesses said.
A Palestinian man was also shot dead as he infiltrated Israel from Gaza and another surrendered, the Israeli military was quoted by the Associated Press news agency as saying.
The diplomatic push follows Sunday's decision by the Israeli cabinet to accept the roadmap and its goal of creating a viable Palestinian state - the first time an Israeli government has ever accepted such a plan, albeit with reservations.
Nearly half the Israeli cabinet either voted against the peace plan or abstained, and ministers set down conditions for accepting it - including a demand that the Palestinians take the first step to end violence.
Before voting, the cabinet also passed a motion rejecting the Palestinian demand of the right of refugees to return to their former homes in Israel - a move which Israel says would demographically destroy the Jewish state.
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