JERUSALEM (Reuters) - Israeli leader Ariel Sharon said on Thursday conditions were right for a "historic breakthrough" on Middle East peace after measures taken by new Palestinian President Mahmoud Abbas to bring calm.

He said that if Palestinians worked to "fight terror," then Israel could move forward with a U.S.-backed peace "road map" meant to lead to a Palestinian state.

"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," Sharon told a business forum.

Palestinians said that in order to help Abbas who faces a strong challenge from militants, the Israelis had agreed in principle to pull back troops from West Bank cities reoccupied during a 4-year- old uprising and to free hundreds of prisoners.

Abbas appeared to suffer a setback in the Gaza Strip where the Islamic militant Hamas group made a strong showing in first-ever municipal elections there, an exit poll showed.

But Palestinian security forces were to widen their control in Gaza by deploying troops in the south of the coastal strip on Friday to prevent militant attacks, Palestinian sources said.

Under orders from Abbas some 2,000 Palestinian troops took up positions in northern Gaza last week for the first time in years where they have curtailed rocket fire at Israel.

In a sign of a new U.S. push for Middle East peace, officials said Secretary of State Condoleezza Rice would visit the region early next month on the first trip of her new job.

A reduction in violence could lead to renewed peace talks under the U.S.-backed road map peace plan, launched in 2003 and stymied by bloodshed and the failure of both sides to meet their promises.

Hopes of progress have been raised by a dip in violence since Abbas was elected on Jan. 9 to succeed Yasser Arafat and began pursuing a truce deal with militant groups.

ABBAS URGES ISRAEL TO ACT

Speaking after talks with U.S. envoy William Burns, Abbas urged Israel to hold its fire and to agree quickly to a cease-fire with militants who insist it must be mutual.

"The Israelis have to respond quickly. We cannot wait for a week or two," Abbas said in the West Bank city of Ramallah.

Burns told reporters the United States was "very encouraged" by steps Abbas has taken toward a "restoration of law and order" that would serve as a basis for a cease-fire.

Israel says it will answer quiet with quiet and has shelved major military operations, but refused to stop selective raids.

In Gaza, soldiers shot dead a mentally retarded Palestinian man they apparently mistook for a militant when he ran toward troops near the Jewish settlement of Netzarim, medics and Israeli sources said.

A senior Palestinian security figure and Abbas confidant, Mohammed Dahlan, said that Israel had agreed "in principle" to withdraw troops from some West Bank cities. Another Palestinian official said Israel had agreed to free 500 of 7,000 security prisoners as a goodwill gesture.

A senior Israeli official confirmed there was a plan for an Israeli pullback from West Bank cities but that the government would not approve it until the Palestinians "come up with a proper plan to implement" it.

The issue of the prisoners would be on the agenda at Abbas´s expected summit with Sharon next month, the official said. A Palestinian official said the meeting may take place on Feb. 8.

Any Israeli confidence-building steps could help bolster Abbas, who still faces the challenge of the militant Islamic groups like Hamas that are sworn to destroying Israel rather than reaching a deal for a state alongside.

The Independent Palestinian Center for Policy and Survey Research said its exit polls of the first Palestinian elections in Gaza showed that Hamas was likely to take three of the four biggest districts in Thursdays vote, including one where Abbas´s Fatah movement had been expected to triumph.

Thousands turned out to vote for candidates vying for 118 seats in 10 municipal councils. Voter turnout topped 80 percent, Palestinian officials said after the polls had closed.

(Additional reporting by Wafa Amr, Diala Saadeh and Cynthia Johnston in Ramallah and Nidal al-Mughrabi in Gaza) (© Reuters 2005 01/27/05)