Meanwhile, the Popular Resistance Committee, a militant group, said an Israeli aircraft struck a Palestinian militant safe house at a beach camp near Gaza City on Monday.
The Palestinian leader phoned Brig. Gen. Abdel Razek Majaide and asked him to return to the office he left last week at Arafat's request, said Nabil Abu Rdeneh, a senior Arafat adviser.
Arafat took the decision to calm the anger that has spilled into the streets of Gaza over the appointment of Moussa Arafat, Rdeneh said. Opponents claimed the appointment perpetuated a system of corruption and cronyism endemic among the Palestinian leadership.
But Moussa Arafat retained a senior security post in Gaza, subordinate to Majaide who has overall authority in both Gaza and the West Bank, the officials said.
Prime Minister Ahmed Qureia, in a call to Arafat, said "it is time to reactivate all our security branches based on the correct principles. It is now time to appoint the right man to the right position."
Qureia also said he stood by his resignation, which he gave to Arafat on Friday after a breakdown of security in Gaza and a wave of kidnappings.
"I have not received a written response," Qureia said, indicating that he did not accept Arafat's verbal rejection of his resignation as final.
He said he wanted to resign because of "the state of chaos and loss of control over the security situation" in the Gaza Strip, which he said was only benefiting the Palestinians' enemies in Israel.
On Sunday night, Palestinian gunmen stormed an intelligence office in one Gaza refugee camp and marched through another, protesting Moussa Arafat's appointment.
But in Gaza City on Monday, hundreds of his supporters marched through the streets, some firing assault rifles into the air — raising the possibility of a violent conflict over the appointment.
"We will protect you by our soul and our blood, our hero Abu Amr," the demonstrators chanted, referring to Yasser Arafat.
The turmoil in Gaza was a grave challenge for Arafat and highlighted sharp rifts between the veteran Palestinian leader and the Cabinet that is supposed to be running the West Bank and Gaza Strip.
In the Rafah refugee camp late Sunday, gunmen exchanged fire with guards at security headquarters and attempted to break into the complex with a bulldozer. The guards wounded three attackers, but there were no casualties among the security forces, staff at the building said.
A Palestinian freelance news reporter on assignment for Reuters news agency was hit by a stray bullet, witnesses said. A Reuters staffer in Jerusalem said Ahmed Babr was shot in the leg during the Rafah firefight and was in stable condition in a local hospital.
Dozens of masked gunmen marched near Moussa Arafat's office in the Nusseirat refugee camp in central Gaza after sundown Sunday, chanting, "No to Moussa Arafat, yes to reform."
Many Palestinians feel Moussa Arafat is a member of the "old guard," steeped in corruption and known as a cruel commander.
It was the most serious internal unrest since the anti-corruption protests of 2003 that forced Arafat to appoint a new government with the first Palestinian prime minister, Mahmoud Abbas. He resigned after only four months.
The turmoil came against the background of Israeli Prime Minister Ariel Sharon's plan to withdraw from Gaza next year, intensifying a struggle for power and influence among the various Palestinian factions.
Sharon said the trouble reinforced his contention that Israel cannot negotiate with the present Palestinian leadership. "If somebody wants to see it better, we should just watch what is happening now in Gaza," he told visiting U.S. Jewish leaders on Sunday. Earlier, he told his Cabinet that the unrest reinforces Israel's need to pull out of Gaza.
Defense Minister Shaul Mofaz called Arafat's reforms "an illusion," and said the Palestinian leader had retained his grip on power. "They are playing musical chairs," Mofaz told Israel Radio.
The Bush administration has also argued that Arafat must be replaced, accusing him of failing to fight terrorism. In May, President Bush said peace could be achieved "if reform-minded Palestinians will step forward and lead toward the establishment of a peaceful Palestinian state."
But CBS News Reporter Robert Berger notes that while Israel detests Arafat, it fears that Palestinian anarchy could be even worse. Terrorist groups like Hamas and Al-Aqsa Martyr's Brigade could step into the vacuum.
The appointment of Arafat's relative deepened the discord between Arafat's generation, which led the Palestinian struggle from exile for decades, and young Palestinians who lived under Israeli occupation and now accuse the old guard of corruption and monopolizing power.
But dissent went beyond the generational divide and spread to the security forces.
Navy chief Gomma Ghali, an Arafat loyalist, handed in his resignation in protest over Moussa Arafat's appointment. On Friday, the head of intelligence and the head of the preventative security resigned over the failure of the Palestinian Authority to tackle corruption or initiate reform. However, Arafat has not accepted the resignations.
In a rare news conference, Moussa Arafat brushed aside protests over his appointment. "I take my orders from His Excellency President Arafat," he said, seated below a huge portrait of his mentor. "He is the only one who can ask me to quit my job."
He said he was ready to "engage in any battle against any potential enemy," and made it clear the enemy could come from within the Palestinian camp.
Up to now the head of the Palestinian intelligence services, Moussa Arafat has a reputation for ruthlessness. He was among the founders of Fatah, Yasser Arafat's faction of the Palestinian Liberation Organization, in 1965 and has stood by his cousin's side since then.
In 1996, during a mass roundup of Hamas and Islamic Jihad militants, Moussa Arafat shaved the heads and beards of the men he imprisoned to humiliate them. Human rights groups accused him of torture.