"This morning, security forces arrested Nour Issa, 27, who is a leader of the deviant thought movement and is from Bureij Camp in central Gaza, along with others," the source said, using a phrase Hamas officials routinely use to refer to militants, including IS.
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The internal security service confirmed on its Facebook page that it had made a number of arrests.
"One of the leaders of the deviant thought has been arrested along with others," it said, without giving a name.
The Islamist Hamas movement has run Gaza for a decade but it has been challenged by small hardline factions, some of them inspired by IS, who advocate a stricter, Salafist interpretation of the faith.
Some have carried out sporadic rocket attacks into Israel in defiance of an informal truce agreed by Hamas.
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In August, a suicide bomber allegedly linked to IS killed a Hamas guard in southern Gaza along the border with Egypt, in a rare attack against the Islamists. Hamas has arrested a number of Salafist and IS-linked figures.
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