The 27-year-old in a sweatsuit limped to the table, heaved himself into a chair and began to talk about how he had been shot. Men from Hamas have begun to assault people they suspect of supporting its chief political rival, Fatah, he said, and on Sunday, he became one of the victims.

It was impossible to verify the man’s account, which he provided on the condition that he remain anonymous, out of concern for his safety. But it came during a week in which leaders of Fatah accused Hamas of harassing and harming its members in the Gaza Strip.

Yasser Abd Rabbo, an ally of the Palestinian president, Mahmoud Abbas, said at a news conference in Ramallah on Thursday that Hamas had “turned its rifles in the direction of Fatah members” after Israel stopped its military offensive on Sunday. Mr. Rabbo accused Hamas of placing Fatah supporters under house arrest and shooting some of them in the legs, an intimidation tactic that it used in the past.

A Hamas spokesman, Fawzi Barhoum, strongly denied the accusation, saying that Fatah was raising the issue to distract attention from the fact that it remained on the sidelines and did not challenge Israel during the three weeks of fighting in Gaza.

Hamas and Fatah have long been bitter rivals. Hamas, a militant Islamic organization, rejects Israel’s right to exist, while Fatah, a more secular group with backing from Western nations, has been receptive to the creation of a separate Palestinian state side by side with Israel.

Hamas, which seized control of Gaza during a brief but bloody civil war in 2007, appears to have emerged from the Israeli offensive with its authority in Gaza firm and its popularity growing in the West Bank.

But members of Fatah contend that Hamas has begun harassing Fatah supporters to reassert its authority in Gaza. The hopes of Mr. Abbas and Egypt for the creation of a unity government that would bring together the two rival groups could be undermined by reprisals.

Taher al-Nunu, a spokesman for the Hamas-led government in Gaza, said it was looking into a few reports of attacks by low-level supporters of the party, which he characterized as score-settling among local clans, actions that were not sanctioned by Hamas.

“Maybe there are some clashes between families,” he said. “We will investigate these cases. There are not a lot.”

A Palestinian human rights worker, who was granted anonymity because of the delicacy of the topic and the preliminary nature of his findings, said he had received reports of about 30 cases of abuse, including as many as five killings. He said he had not yet been able to verify each case.

Mr. Nunu vehemently denied reports that anyone had been killed. “There are no people from Fatah killed by anyone,” he said. “Let them give us just one name.”

The man in the sweatsuit said in an interview that he had been forced into a car by three men wearing masks while he was walking to his cousin’s house at dusk on Sunday. The men accused him of being happy that Israel had attacked Hamas, and they took him to the prime minister’s palace, which had been destroyed in an Israeli airstrike, he said. There they shot both of his legs just under the knee.

“It hurt like fire,” he said, pulling up the legs of his sweatpants to display thick bandages soaked with blood. He crawled to the road, he said, and someone gave him a ride to the hospital.

The motive for the shooting was not clear. The man said that he was a shoemaker and that he supported Fatah, but was not formally a member. The real target, he said, may have been his cousin, who is an activist in Fatah.

Some Fatah members said in interviews that some of those being sought had been singled out for having handed out sweets in celebration of Israel’s war on Hamas.

Nor was it clear how widespread the attacks were. Mr. Rabbo, the ally of the Palestinian president, said 200 people had been harassed and abused, but the human rights worker estimated that the number was much lower.

Many Fatah members and supporters said in interviews that Hamas might feel somewhat weakened by the Israeli offensive and was concerned that its political rivals not take advantage of the disorder created by the war.

The Palestinian human rights worker shared that view. “The internal security department is sending a very clear and strong message to Fatah to be quiet,” he said.

The shoemaker’s cousin, who actively supports Fatah, said that he had been moving from house to house after Hamas members searched his home on Sunday while he was out.

“They’re afraid that Fatah will take advantage of the chaos to come back to power,” the cousin said. “The message is: Stay at home. Be afraid. We didn’t lose power.”

A few patterns did seem to be emerging. Those who had Fatah and Hamas political affiliations within a single family tended not to be targets. And the cousin said it was not the central Hamas leadership that was looking for him, but only people from the party’s neighborhood branch, confirming, in part, what Mr. Nunu of the Gaza government said.

Several people said Hamas had given children cellphone credits to keep tabs on them. They are called “drones,” and when they pass, everyone knows to stop talking, said a man in Bureij, a town south of Gaza City, who said he had been told by local Hamas supporters to stay inside his house.

Typical of the political divisions here, people in Gaza had varying opinions about whether Hamas was carrying out reprisals against Fatah members.

“The Fatah people in Ramallah are saying this for a reason,” said Sami Nasir, a Fatah supporter who was smoking a cigarette in front of Al Khoznadar restaurant. “It’s happening. A lot of Fatah sympathizers are hiding at home these days.”

Maher al-Hawalani, an elegant man with a neatly trimmed beard, who said he was a Hamas sympathizer, disagreed. “Does the Fatah have anything to do with the war?” he asked. “No! So why would Hamas go after them?”