He reportedly called for the territory to be governed purely by sharia, or Islamic law.
Moussa was killed in the fighting, apparently blowing himself up.
Hamas officials said one of his sons was also killed, along with an aide named Khaled Banat, known as Abu Mohammed al-Mujahir, a Syrian who they said was of Palestinian origin.
Hamas said six of its fighters and six civilians, including an 11-year-old girl, were among the dead. Over 100 people were injured in the fighting.
Residents said the Ibn Taymea mosque where Moussa preached on Friday to a hundred or so supporters, some armed and dressed like Taliban fighters, was hit by grenades and Moussa's house destroyed.
The violence in Rafah was the most serious inter-factional Palestinian fighting in the territory since Hamas seized power two years ago, pushing out the Fatah party of Mahmoud Abbas, the Palestinian president.
But in exerting its control on the Strip and battling the group, Palestinian analysts said Hamas was also demonstrating to the West its willingness to suppress radical groups.
Hamas is considered a "terrorist" organisation by the US and most Western powers shun the group, which won a parliamentary election in 2006.
Jund Ansar Allah is one of several small groups in Gaza to espouse al-Qaeda sympathies.
"A number of these extremist groups have flourished over the Gaza Strip over the past two years," Mkhaimer Abusada, a professor of political science at Gaza's Al-Azhar university, told Al Jazeera.
"Some extremist Palestinian Muslim groups do not see Hamas as representing Islam, and they are calling on Hamas to represent Islam or they will take matters into their own hands as we saw in the past two days."
Several Rafah residents also voiced disquiet at the Hamas response and said they fear reprisals.
"It is wrong for anyone to take the law into their own hands and impose Islamic law," one man, who gave his name as Ali, said by telephone.
"But even so, people shouldn't be killed like this. I don't think this is the end. The fundamentalists will hit back."
Jund Ansar Allah first made its presence known with a border raid against an Israeli base in June, when some of its fighters rode into battle on horseback.