Israeli Prime Minister Ariel Sharon appears to have eased his preconditions for talks with the Palestinians.
Ariel Sharon set Palestinians a new test
Mr Sharon said the Palestinian leadership no longer had to tackle militant groups ahead of the resumption of negotiations.
Some of Mr Sharon's Likud colleagues criticised the move as a major concession to the Palestinians.
It came as diplomatic moves to support peace efforts are stepped up following Yasser Arafat's death.
In a speech on Thursday, Mr Sharon proposed a new test for the new Palestinian leadership.
He called for an end to "constant poisonous
incitement and propaganda" in Palestinian media and education.
He said Israel should not waive demands to disarm Palestinians and dismantle terrorist organisations, "but it's clear that this is a more complicated process".
"I don't intend to waste time" in starting up talks, he said.
Some Likud politicians said it was a significant change of policy.
Agriculture Minister Israel Katz described Mr Sharon's move as a "new departure".
And deputy commerce and industry minister Michael Ratson said: "The prime minister strays to the left. He always vowed to wage an uncompromising war on terrorism and then he narrows the goalposts in a way he never did before."
Mr Sharon's spokesman, Raanan Gissin, said the prime minister wanted to show that "Israel is ready to move forward".
Palestinians said Israel had to offer more.
Asked about how to handle militants, interim Palestinian
leader Mahmoud Abbas said: "We have our share to do, but they [the Israelis] have more."
Mr Abbas also said Palestinians must end the "armed chaos" in the Gaza Strip and West Bank, as the territories prepare to elect Arafat's successor on 9 January.
He has been meeting militant groups, including Hamas, in an effort to secure a ceasefire in the run-up to the vote - though it is not clear if he has won any assurances.
Amid new hopes of peace moves in the region, Israel and the Palestinians are expecting visits by US Secretary of State Colin Powell, and the Russian and British foreign ministers, in the coming week.
Also on Friday, Israeli soldiers killed two Palestinians near the town of Rafah in the southern Gaza Strip.
The Israeli army said its troops opened fire after spotting the two men crawling towards a military post close to Israeli-controlled territory between Egypt and Gaza.