The group is believed to be the military wing of the Popular Resistance Committees.
The Associated Press also quoted a spokesman for the committees as claiming responsibility of the assassination on Wednesday.
The group said it killed Major-General Arafat, a cousin of the late Yasser Arafat, on Wednesday morning to punish him for alleged corruption after the Palestinian security forces had taken no action against him.
"We have implemented God's law," spokesman Mohammed Abdel-Al said on Wednesday.
However, the director of Palestinian military intelligence in Nablus doubted the ability of al-Nasir Salah al-Din Brigades to launch the offensive, saying that the group was "incapable of carrying out such a big operation in Gaza".
Speaking to Aljazeera on Wednesday, Brigadier Maher Fares said the assailants had been provided help in carrying out the killing, and demanded that the Palestinian Interior Minister resign.
"I believe that the Popular Resistance Committees or whoever really was behind the assassination, was provided some form of assistance to commit this crime," he told Aljazeera.
"I believe that the Popular Resistance Committees or whoever really was behind the assassination, was provided some form of assistance to commit this crime"
Brigadier Maher Fares, director, military intelligence in Nablus
"The killing involved the firing of rocket-propelled grenades and detonation of explosive devices. The clashes lasted for around 45 minutes despite the proximity of Mussa Arafat's house to the headquarters of President Abbas and other security departments," he said.
Fares continued: "This means that there is a clear inadequacy in the efforts of the Palestinian Interior Ministry and all security apparatuses in the area.
"I do not hold the Palestinian interior minister responsible for the assassination, but for the inadequacy of efforts."
Masked armed men
According to Palestinian security sources, Arafat was killed at his home overnight during an exchange of fire between the attackers and his bodyguards.
Mussa Arafat was killed outside
his home in the Gaza Strip
Aljazeera's correspondent in Gaza Wail al-Dahduh learned that about 80 masked armed men, travelling in a convoy of 20 vehicles, took positions on all roads leading to Arafat's house in Gaza.
The men then stormed Arafat's house using gunfire, rocket-propelled grenades, stun grenades and other explosive devices, before storming it, al-Dahduh said.
Arafat and his son were led to the gate of the house, where he was shot. His son was kidnapped by the attackers.
Three of Arafat's bodyguards were injured in the attack, while others were handcuffed by the attackers, the correspondent added.
Relieved of duties
Arafat's death comes as Palestinian security forces prepare to take control of the Gaza Strip which the Israeli army has said it would vacate completely by 15 September.
The 65-year-old Arafat was removed by Abbas from his government position in April this year after being linked to corruption charges, but was retained as an adviser on military affairs with ministerial rank.
Mussa Arafat was removed from
office in April this year
Arafat was a founder of the ruling Fatah movement and was a senior official in the Fatah Revolutionary Council, a top policy-making body. The council had been scheduled to meet later on Wednesday.
On Wednesday, Abbas condemned the killing and vowed his security forces would do everything it could to bring those responsible to justice.
"President Mahmoud Abbas condemned the assassination of General Mussa Arafat," said the Palestinian Authority in a statement carried by the official WAFA news agency.
Mahmoud Abbas has vowed to
bring those responsible to justice
"The Interior Ministry and security services will make every effort necessary to find those responsible for this crime and bring them to justice," the statement quoted Abbas as saying.
Abbas convened an emergency meeting of his national security council to discuss how best to assert control over the lawless Gaza Strip with his forces preparing to take control following the imminent departure of Israeli troops.
Aljazeera's correspondent al-Dahduh said the Palestinian president's office is convinced the incident is the most serious attack so far and threatens all Palestinian Authority staff.
Known to have many enemies, Mussa Arafat survived an assassination attempt in July 2003 when attackers threw a grenade towards his car.
Yasser Arafat appointed his cousin head of security in July 2004 to loud protests in the Gaza Strip, and even within Yasser Arafat's own Fatah movement.
As head of military intelligence, he was accused of taking part in the repression of armed groups.