GAZA (Reuters) - Hamas arrested three Palestinians who fired rockets into Israel from the Gaza Strip on Thursday, a militant faction said, in the first such detentions since the Islamist group and Israel agreed a truce last month.

Al-Aqsa Martyrs Brigades, a group linked to President Mahmoud Abbas\'s Fatah group, said Hamas men pursued its members after the attack and "abducted them" in Jabalya refugee camp. No one was hurt in the strike with two rockets on southern Israel.

"We demand their immediate release," said Abu Qusai, a brigades spokesman.

Hamas official Sami Abu Zuhri said: "We stress that all parties should maintain the national agreement that was reached with a consensus."

Hamas, which seized control of the Gaza Strip a year ago after routing forces loyal to the secular Fatah group, had previously said it would not use force against other militants who violate the truce.

Al-Aqsa said it launched the rockets in retaliation for the Israeli army\'s killing of an unarmed member of the group as he tried to cross a border fence into Israel earlier in the day.

His death marked the first fatality along the Israel-Gaza border since a June 19 Egyptian-brokered ceasefire.

An Israeli army spokesman said soldiers shot the man after he ignored their calls to stop and only saw later that he had been unarmed.

The ceasefire deal calls on Hamas to prevent cross-border rocket fire and attacks from the Gaza Strip, and for Israel to halt its raids and ease an economic blockade.

"If a total cessation of fire from Gaza, as committed in the calm, is not implemented, the calm has no possibility to succeed," Israeli Prime Minister Ehud Olmert\'s spokesman, Mark Regev, said.

Israel tightened restrictions on the passage of people and goods to and from the impoverished territory after Hamas\'s takeover. United Nations officials said Gaza\'s goods crossings were still shut rather often despite the truce.

"There is not enough fuel, not enough food, there is not enough of anything," John Ging, an official with the U.N. Relief and Works Agency (UNRWA) that aids refugees, said in Gaza.

Although Israel has responded to cross-border rocket fire by frequently shutting Gaza\'s crossings, records compiled by Western officials show up to a 44 percent increase in goods imports in recent weeks, including a 30 percent rise in fuel.

NABLUS

In the occupied West Bank, Palestinian Prime Minister Salam Fayyad visited the city of Nablus, where Israeli troops had raided several charity groups and a medical clinic and closed down a local television station, Palestinian officials said.

Over the past several days, Israel has raided 15 Nablus charities suspected of being linked to Hamas.

Speaking to shop owners inside a mall that Israel has ordered closed, Fayyad said: "It should be known clearly that the Israeli army orders and decisions are not valid and don\'t have any basis. We will deal with them as if they don\'t exist."

"Shopkeepers are invited to open their stores and ignore the Israeli decision," he added.

Senior Hamas leader Ismail Haniyeh accused Palestinian Authority officials of backing the Israeli operations.

But Palestinian Interior Minister Abdel-Razzak Yahya condemned the raids and said the Palestinian Authority would continue dealing with institutions that Israel ordered closed.

Earlier on Thursday, Fayyad visited a town where protests against Israel\'s West Bank barrier led to a two-day Israeli curfew in the community of 5,000 that was lifted on Tuesday.

Fayyad traveled to Nilin, 20 km (12 miles) east of Tel Aviv a day after the fourth anniversary of a ruling by the International Court of Justice that termed the network of razor-wire tipped fences and cement walls illegal.

(Additional reporting by Atef Sa\'ad in Nablus and Mohammed Assadi in Ramallah; Writing by Jeffrey Heller in Jerusalem; Editing by Sami Aboudi)