Mohammed Abdel Al, a spokesman for al-Nasir Salah al-Din Brigades, the military wing of the Popular Resistance Committees, said the killing of Arafat in Gaza on Tuesday was about putting an end to what he called terrorism practised by some elements within the Palestinian Authority (PA).
Mussa Arafat 65, a cousin of the late president Yasser Arafat, was a high-ranking and feared security chief before being removed by President Mahmoud Abbas in April, after being linked to corruption charges.
Al-Nasir Salah al-Din Brigades also kidnapped Mussa Arafat's son.
"Everyone who has been unjust to the Palestinian people is a potential target. We want to preserve the rights of the Palestinian citizens and protect them from these people," Abdel-Al, also known as Abu Abeer, told Aljazeera.net on Wednesday.
"[Mussa Arafat] stole people's land and money and killed many people. And his son is no better. There are very many private issues that he was involved in that we will discuss in detail at a later time," Abdel-Al said.
"We consider the Israeli withdrawal from the Gaza Strip an accomplishment of the Palestinian resistance, and ending the corruption will also, we hope, be an accomplishment of the resistance.
He added: "Every corrupt person must atone for and confess to his sins publicly and return to the people what they stole from them or suffer the consequences at the hands of the mujahidin."
Abdel-Al warned the PA to hold people to account and that the Brigades would act if it failed to do so.
"Everyone who has been unjust to the Palestinian people is a potential target"
al-Nasir Salah al-Din Brigades spokesman
"We consider [people like Mussa Arafat] traitors and supporters of the Zionists and we have to get rid of them from their roots," he told Aljazeera.net.
"We consider the Zionist withdrawal from Gaza a victory, but we cannot hold on to this victory if the corruption continues."
On the fate of Arafat's kidnapped son, Abdel-Al said that he was under interrogation and said that if he confessed to his wrongdoings, he would be handed over to proper judicial authorities for trial.
The PA condemned the attack, calling it a "dangerous crime" and promised a speedy investigation overseen by Nasser Yusuf, head of national security.
A spokesman for the Ministry of the Interior said the attack was a "dangerous escalation" in the internal security situation in Gaza, and promised the perpetrator's would not go unpunished.
But Abdel-Al countered the condemnation by the PA, saying the Popular Resistance Committees was "not afraid of any human being. We do not want to face off with the PA, but what the PA represents now leaves us no choice".
Meanwhile, Islamic resistance groups such as Hamas and Islamic Jihad also condemned the attack, saying the use of assassinations against Palestinians was unacceptable, regardless of the target.
"There needs to be one law that applies equally to everyone, not just to one or two factions," said Sami Abu Zuhri, a spokesperson for Hamas.