Israeli Prime Minister Ariel Sharon has said he is "very pleased" with measures Palestinian leader Mahmoud Abbas has taken to lessen the threat of violence.
Palestinians say the polls answer foreign calls for democratisation
Mr Sharon said conditions were right for a "historic breakthrough" between Israel and the Palestinians.
Mr Abbas has brokered a temporary ceasefire with militants and banned Palestinians from carrying weapons.
Palestinians in parts of Gaza have meanwhile been voting in historic local polls for mayors and council members.
Exit polls suggested candidates from the Hamas militant group won most seats in three out of four of the biggest districts where they were held.
BBC Gaza correspondent Alan Johnston says Hamas is showing how the bomb and the ballot box can both play a part in its strategy.
He said Palestinian enthusiasm for the polls stems partly from the belief that they are strengthening the case for a state of their own and for an end to the Israeli occupation.
In a speech on Thursday evening, Mr Sharon praised recent Palestinian measures to end the threat of militant attacks - a prerequisite, Israel says, for any peace process.
"If the Palestinians take comprehensive action to stop the terror, violence, and incitement, we'll be able to make progress," he said.
"I believe the conditions have been created that will enable us and the Palestinians to attain the historic breakthrough in our relations, a breakthrough that will lead us to quiet and security, and in the future even to the yearned-for peace."
Formed in 1989
Spearheads suicide attacks against Israelis
Aims to establish an Islamic state in all of historic Palestine
Leaders targeted for assassination by Israel
Earlier Mr Sharon said he aimed to be "accommodating" Mr Abbas, but to remain "vigilant".
Speaking after talks with US State Department official William Burns, Mr Abbas meanwhile warned the situation could "not last for long" if Israel did not offer a swift halt to military operations - a key condition for a full ceasefire from the militants.
Mr Abbas has also issued a ban on civilians carrying weapons in public - seen largely as a symbolic step towards strengthening the power of Palestinian security forces and curbing the clout of Palestinian militants.
Israeli Foreign Minister Silvan Shalom has however warned that the truce negotiated between Mr Abbas and militants is a "ticking bomb which will blow up in our faces".
In other developments:
- Israeli troops reportedly shoot dead a mentally disturbed Palestinian man who approaches their outpost near Gaza City
- Palestinian police deny an Israeli report they have begun a planned deployment in southern Gaza, blaming the delay on technical hitches
- Israel agrees to release some 500 Palestinian prisoners, according to a Palestinian official
- Militants claiming to be from the al-Aqsa Martyrs' Brigade say they will end their truce within a day if Israel fails to end military operations, after an Israeli raid leaves one Palestinian dead
- On Wednesday, a three-year-old Palestinian girl was killed when Israeli troops opened fire in retaliation for a rocket attack on southern Israel.