Followers of the group said Abdul Latif-Moussa blew himself up in a crowd of Hamas police, but Hamas has denied this.
Six Hamas fighters, including a senior commander, and one civilian died. The rest of those killed were from Jund Ansar Allah.
About 120 people were injured, with some in a critical condition, the BBC's Rushdi Abu Alouf says.
The Hamas spokesman, Tahir al-Nunu, said: "We hold Abdul-Latif Moussa and his followers fully responsible for what happened because of his hasty declaration during Friday prayers of a so-called 'Islamic emirate'."
The Jund Ansar Allah (Soldiers of the Followers of God) is thought to be inspired by al-Qaeda.
The battle lasted several hours
Mr Nunu said: "Anyone who belongs to this group has to immediately hand himself and his weapons over to the Palestinian police and security forces."
Another Hamas official, Sami Abu Zuhri, branded the cleric's speech "wrong thinking".
Hamas fighters on Friday fired rocket-propelled grenades at Ibn-Taymiyah mosque, where at least 100 Jund Ansar Allah supporters were holed up.
These declarations [of an Islamic emirate] are aimed towards incitement against the Gaza Strip
Ismail Haniya, leader of Hamas in Gaza
The entire neighbourhood was sealed off as the shooting continued after dark - in what was one of the most violent incidents in the Hamas-controlled Gaza Strip since an Israeli offensive in December and January.
Abdul-Latif Moussa and his armed supporters had sworn to fight to the death rather than hand over authority of the mosque to Hamas.
During his own Friday sermon, the leader of Hamas in Gaza, Ismail Haniya, dismissed Mr Moussa's comments.
"These declarations [of an Islamic emirate] are aimed towards incitement against the Gaza Strip and an attempt at recruiting an international alliance against the Gaza Strip.
"And we warn those who are behind these Israeli Zionist declarations: the Gaza Strip only contains its people."
Jund Ansar Allah gained some prominence two months ago when it staged a failed attack on horseback on a border crossing between Gaza and Israel.
The group is very critical of Hamas, which seized control of Gaza in 2007, accusing the Islamist group of not being Islamist enough.
Hamas has cracked down hard on al-Qaeda-inspired groups in the past, the BBC's Middle East correspondent Katya Adler says.
Hamas is concerned they may attract more extremist members, and has forbidden anyone except what it describes as Hamas security personnel from carrying weapons in Gaza, our correspondent says.
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