"In the coming days, the Israeli prime minister and the Palestinian prime minister will meet and begin talks," Sharon told members of Italy's Jewish community during a state visit that began here Monday.
A meeting between Sharon and Qureia would be the first since the Palestinian took office over a month ago. Sharon met with Qureia's predecessor, Mahmoud Abbas, four times but Palestinians complained that there were few concrete results from the meetings.
Abbas resigned Sept. 6 after disagreements with long-time Palestinian leader Yasser Arafat.
Sharon is under growing pressure at home and abroad to try to break the deadlock over the U.S.-backed "road map" peace plan.
Last week, four former directors of Israel's Shin Bet security service warned that Israel is headed for disaster if the conflict with the Palestinians is not settled soon. They also accused Sharon of stalling in order to avoid making concessions.
At the same time, a symbolic peace deal negotiated by prominent Israelis and Palestinians has won attention and praise, including from Secretary of State Colin Powell — an apparent signal of U.S. displeasure with Sharon's policies.
On Monday, Russian Foreign Minister Igor Ivanov also welcomed the "Geneva Accord," saying it complemented the road map because it provides a final settlement. Ivanov sent a letter to the organizers of the initiative.
The Egyptian intelligence chief working to broker a Mideast truce said earlier Monday he had received "positive" signals from Israel and invited Palestinian militant factions to Cairo for talks next week, a Palestinian official said.
Omar Suleiman met with the head of Israel's Mossad intelligence agency and other officials as well as Palestinian Prime Minister Ahmed Qureia and Arafat. Qureia has said he wants to win agreement from the militant groups to halt attacks on Israelis, then to negotiate a cease-fire with Israeli Prime Minister Ariel Sharon.
Suleiman told the Palestinians that Israeli leaders, while not giving any assurances, appeared receptive, Palestinian Foreign Minister Nabil Shaath said.
"He did say that there is an opportunity that must be taken advantage of. There is a positive atmosphere and a new language," Shaath said. "He told us that he is optimistic."
In the past, Israel has said it will only halt military strikes if Palestinian security forces begin dismantling militant groups, including Hamas and Islamic Jihad. However, Israel has signaled in recent weeks it is willing to test a truce for a limited period, without insisting on an immediate crackdown on armed groups.
A truce between Israelis and Palestinians is considered essential for reviving the peace plan, which envisions Palestinian statehood by 2005. Yet expectations of progress remain low, with the Bush administration expected to be preoccupied with the 2004 election campaign.
As part of renewed cease-fire efforts, Suleiman met Monday with Palestinian Prime Minister Ahmed Qureia and veteran leader Yasser Arafat. Qureia has said he wants the militant group to agree to halt attacks on Israelis, then negotiate a cease-fire with Sharon.
Israeli Mossad intelligence service chief Meir Dagan told a parliament hearing Monday Iran's likely nuclear capability is the greatest threat that Israel has faced since its founding in 1948.
He also said Iran supports terrorist organizations such as Hamas, the Islamic Jihad, and Hezbollah, as well as the missiles that militants have deployed in southern Lebanon.
Suleiman, when asked about truce prospects as he left Arafat's office, said, "Hopefully, there is a cease-fire and dialogue and many good things."
Suleiman also held talks with the U.S. ambassador to Israel, Dan Kurtzer.
Kurtzer said Monday that the challenge facing Israelis and Palestinians was to begin to "flesh out the content of the road map."
He added that the road map "still has life."
Speaking to delegates of the General Assembly of the United Jewish Communities meeting in Jerusalem, Kurtzer said the Bush administration is not opposed to the concept of a security barrier, just the route proposed.
The Israeli security services are divided over whether to accept a truce without a crackdown on militants. The military favors doing so while the Shin Bet security service opposes it, warning that militants would use the time to rebuild.
A Hamas leader, Mousa Abu Marzook, told Egyptian intelligence officials in Cairo earlier this month that his group was ready for a truce if it was backed by the international community and Israel publicly commits to it.
Nafez Azzam, an Islamic Jihad spokesman in Gaza, said Monday his group also was willing to halt attack on Israelis "if Israel stops its attacks on our people."
The "road map" requires the Palestinians to dismantle militant groups, but leaders have said they will not use force for fear of triggering internal fighting. Israel has to dismantle dozens of illegal settlement outposts and freeze settlement construction.