* Hamas security out in force, say in full control

* Amid devastation of battle, neighbours praise dead cleric

* Supporters of Qaeda-aligned cleric warn they may hit back

(Adds comment, detail)

By Nidal al-Mughrabi

RAFAH, Gaza Strip, Aug 16 (Reuters) - Hamas militiamen were out in strength in the Gaza Strip on Sunday, asserting their authority over the Palestinian enclave after a bloody showdown with a rival Islamist splinter group aligned with al Qaeda.

In the southern town of Rafah, by the border with Egypt, residents sifted through the rubble of apartment buildings blown up during hours of fighting on Friday and Saturday that left up to 28 dead and a mosque ravaged by bullets and grenades.

Neighbours who knew Abdel-Latif Moussa, whose declaration of Islamic rule from the mosque on Friday triggered the onslaught by fellow Islamists from Hamas, recalled a gentle, devout man.

Many bemoaned the bloodiest violence among Palestinians since 2007. Some forecast reprisals by more young men, some of them former Hamas fighters now disillusioned by its attempts to reach out to the West and negotiate an end to Gaza's isolation.

In a statement on a Web site used by al Qaeda-allied groups from Gaza, a shadowy figure using the nom de guerre Abu Mohammed al-Maqdessi made clear there was anger against Hamas: "The slaughterer in Gaza is Hamas. It is the one holding the knife."

But Hamas, which ousted Western-backed Palestinian President Mahmoud Abbas and his forces from the Israeli-blockaded coastal strip two years ago, insisted the chapter was closed with the death of the physician-preacher who led the "Warriors of God".

"The situation in the Gaza Strip is fully under control," Hamas Interior Ministry spokesman Ehab al-Ghsain said.

Blue-uniformed policemen manned roadblocks and checked cars.

Fighters from Hamas's military wing, in facemasks and green Islamic headbands, veterans of January's war with Israel, kept watch discreetly on their fellow Palestinians as residents cleaned up around the devastated Ibn Taymea mosque in Rafah.

Ghsain dismissed chatter on the Internet about Palestinians being warned to steer clear of Hamas police stations for fear of suicide attacks by Moussa's followers. Security forces were tracking down "some individuals", Ghsain said. Hamas would also aim to "re-educate" those who strayed from "moderate Islam".

"They represent no security threat," Ghsain insisted.

INFLUENCE

Though the numbers involved in Moussa's Jund Ansar Allah (Warriors of God) and other secretive groups, such as the Army of Islam, are hard to gauge, analysts tend to agree they are limited in terms of men under arms, possibly in the hundreds.

Their influence, however, is significant, analysts say.

By tapping into widespread frustration with the economic hardships and Israeli attacks seen under Hamas rule, along with appealing to traditionalist ideas, they can attract some Hamas supporters and put a brake on Hamas efforts to reach out, both to its secular rivals Fatah in the West Bank and to the West.

Few see isolated Gaza as an international base for al Qaeda.

President Abbas derided Hamas's rule in Gaza as "anarchy" but said his Fatah party was ready to talk about ending the schism that has paralysed peace negotiations with Israel.

In Israel, media reports of the weekend violence focused on the violent tactics employed by both sides, including reports that Jund Ansar Allah used suicide bombs against Hamas.

Many Israelis, including right-wing Prime Minister Benjamin Netanyahu, cite violence from and within Gaza since Israel pulled out troops in 2005 in arguing against ending occupation of the West Bank -- a key element in U.S.-backed peace talks.

In the dusty streets of Rafah, on the border with Egypt's Sinai desert where a network of tunnels keeps Gaza supplied in the face of the blockade, there were scenes of devastation.

The four-storey apartment block where Hamas said Moussa and a Syrian lieutenant blew themselves up, was a heap of rubble -- the result, neighbours said, of demolition charges laid by Hamas after the fighting ended. It looked just like the rubble that is all that remains of nearby homes destroyed by Israeli missiles.

The substantial, two-storey, white mosque across the way, where Moussa, or Abu al-Nour al-Maqdessi, had on Friday declared an Islamic "emirate", was peppered with bullet and blast holes.

Its tall minaret, now topped by a green Hamas flag, was particularly ravaged -- signs, locals said, of a last stand by dissident Hamas fighters against their former comrades.

While mourning tents were set up in Rafah for six fallen Hamas policemen, relatives said the families of the radical fighters had been ordered to bury their dead in the night.

In a mark of the tight network of relations in Gaza, one man said he had lost a relative on either side of the battle.

"I don't like them dying that way as both were Muslims. I'd rather they had died fighting the Jews," said Ala al-Louqa, 26, whose brother was in Hamas and whose cousin fought for Moussa.

"I'm confused about Islam now. Who's right and who's wrong?"

Another young man, who gave no name but said he supported Moussa, warned: "There may be a backlash. Hamas hurt itself when it killed the sheikh and a great number of the best Muslims." (Additional reporting by Alastair Macdonald in Rafah; Editing by Janet Lawrence) (For blogs and links on Israeli politics and other Israeli and Palestinian news, go to http://blogs.reuters.com/axismundi)

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