A senior Israeli official said: "Israel will not talk about a cease-fire officially. We don't go into a cease-fire with terrorist organizations. What we're talking about is understandings."
For instance, "there will not be targeted killings unless there is a ticking bomb," meaning an imminent attack, said the official, who declined to be named because of the sensitivity of discussions. "If tomorrow the new head of Hamas walks on the street of Gaza, he will not be targeted by Israel. But tomorrow if a Hamas terrorist is on the way to Jerusalem, he will be targeted."
Some Palestinian political analysts said that Thursday's local elections in 10 Gaza communities would help usher in an era of accountable, democratic government that would have a moderating effect on Islamic extremist groups.
"I am sure this democratic process will diminish the influence and effect of these religious parties, but we have to get them into the political system, and then they will have to act according to the rule of law and democracy, and that will be a great achievement not only for Palestine, but for the whole region," said Raji Sourani, a human rights activist in Gaza.
According to exit polling by the Center for Palestinian Research and Studies, voters in the northern Gaza town of Beit Hanoun, which has been devastated by Israeli military operations, awarded Hamas six seats, while Fatah, the political movement of Yasser Arafat, came in second with three. In Maghazi, the fourth town surveyed, Fatah won 12 seats and Hamas one.
Rather than run under their official names, every party chose a different name for its block of candidates. Fatah's candidates were on the Martyrs' List, while Hamas called its slate the Change and Reform List.
In Deir el-Balah -- with about 60,000 residents, the largest town where elections were held Thursday -- streets were lined with colorful flags and posters depicting the founders of the two main parties: Fatah's Arafat, who died in November, and Hamas's Sheik Ahmed Yassin, who was killed in an Israeli missile strike last April.
Hamas, which has conducted numerous suicide bombing attacks against Israelis and is listed as a terrorist organization by the United States, plastered buildings with posters, strung signs between streetlights and inundated polling places with campaign workers in green baseball caps. Block after block was decorated with party messages clearly targeting what opinion surveys show is widespread disenchantment with cronyism and corruption in the Fatah-dominated Palestinian Authority.
Palestinians in Gaza, which before its occupation by Israel in 1967 was ruled by Egypt, have never voted in local elections. The previous council here was entirely appointed, and entirely Fatah.
"The old council belonged to one group, and look at the streets, the corruption, the lack of services," said Rewaa Mohammed Abu Hewishel, 19, who had adorned her black burqa with a bright green sash reading, "Change and Reform Islam is the solution."
"People are sick of corruption," said her friend, Nour Abu Sbetan, also dressed in a burqa. "We want to build a new Islamic state."
Correspondent Molly Moore and researcher Samuel Sockol in Jerusalem contributed to this report.