BETHLEHEM, West Bank — The Palestinians’ ruling Fatah Party appeared to be bouncing back from corruption and inefficiency charges to show strength in local races that could provide momentum toward a summer parliamentary election showdown with Hamas.

Partial and unofficial returns from Thursday’s elections in 84 towns and villages in the West Bank and Gaza Strip showed Fatah leading the race with 56 percent of the votes compared with 33 percent for the Islamic militant group, election officials said Friday.

Hamas was winning in pockets in the territories, however. In Rafah on the Gaza-Egypt border, the town most battered in four years of Palestinian-Israeli violence, Hamas had 10 seats compared to five for Fatah, according to partial results. In Beit Lahiya, another hard-hit Gaza town, Hamas won seven seats with all votes counted, compared to six for Fatah.

Preliminary results showed Hamas winning all 15 city council seats in Qalqiliya, with all votes counted.

Official results are expected Sunday, but Fatah activists had already taken to the streets of Gaza late Thursday to celebrate.

The elections are hard to interpret, because tribal rivalries and local matters counted at least as much as party affiliations. The real test is July 17, when Palestinians vote for a new parliament after 11 years — and Hamas fields candidates for the first time.

With the late Yasser Arafat and his mythical, charismatic leadership out of the picture, Palestinians are openly criticizing the Fatah Party he headed and the government he created for widespread corruption, nepotism and inefficiency — and his successor, Mahmoud Abbas, could pay the price despite efforts to clean up the government and its security forces.

Hamas has set itself up patiently with years of welfare programs for impoverished Palestinians, especially in Gaza, and is poised to take advantage of voter disaffection with Fatah.

“We are very honest and work much more than the others,” said Khaled Saada, a Hamas candidate for Bethlehem town council, citing schools, clinics and orphanages run by his group. “It is confirmed that we are much better at helping people.”

Hamas participation in elections bolsters Abbas’ hopes to co-opt the militants into mainstream Palestinian politics. But a strong Hamas showing in Thursday’s and other votes, especially this summer’s parliamentary ballot, would harm Abbas’ plans for a renewed Mideast peace track.

Hamas is sworn to Israel’s destruction and has carried out dozens of suicide bombings in the Jewish state. However, it agreed to a temporary cease-fire along with other militant groups in March.

Fatah took a beating in two earlier rounds of local voting, and Shikaki said party leaders learned their lessons from that. Fatah “did a good job preparing for this election by unifying itself and making a strong team with effective people,” he said.

Turnout was strong, with 70 percent of voters going to the polls in the West Bank and 80 percent in Gaza, according to election officials. The only reported incident of violence came from a town in central Gaza, where Hamas backers exchanged fire with police. One person was wounded. Each side blamed the other for the clash.

In Atara, a village near Ramallah in the West Bank, Palestinian security said Fatah gunmen raided election headquarters and stole the ballot boxes. Hamas activists said Fatah feared Hamas had won.

In the battered Rafah refugee camp, Salma Abu Gazar, 51, said she voted for Hamas because she wants change.

“We want clean streets and new projects, like sewage treatment, and our destroyed homes to be rebuilt. I believe that Fatah will not do anything. They will monopolize everything like they have done before,” she said.

However, Anton Salman, a leading Fatah candidate mentioned as a possible mayor for Bethlehem, predicted his party will reverse the downward trends.

Since the January elections, he said, “Fatah has built a new partnership with the local community in Bethlehem … Fatah got the message and we are running this election with people who have experience on the ground.”

In violence after nightfall Thursday, Palestinians fired two rockets at the Israeli town of Sderot just outside Gaza late Thursday, hitting a house. No one was hurt. Israeli official David Baker charged that the Palestinian Authority is freeing suspects and “allowing them to perpetrate additional acts of terror. This has to stop.”

Palestinian security officials promised to investigate.