CAIRO (Reuters) - Islamic State insurgents threatened on Tuesday to turn the Gaza Strip into another of their Middle East fiefdoms, accusing Hamas, the organization that rules the Palestinian territory, of being insufficiently stringent about religious enforcement.

The video statement, issued from an Islamic State stronghold in Syria, was a rare public challenge to Hamas, which has been cracking down on jihadis in Gaza who oppose its truces with Israel and reconciliation with the U.S.-backed rival Palestinian faction Fatah.

"We will uproot the state of the Jews (Israel) and you and Fatah, and all of the secularists are nothing and you will be over-run by our creeping multitudes," said a masked Islamic State member in the message addressed to the "tyrants of Hamas".

"The rule of sharia (Islamic law) will be implemented in Gaza, in spite of you. We swear that what is happening in the Levant today, and in particular the Yarmouk camp, will happen in Gaza," he said, referring to Islamic State advances in Syria, including in a Damascus district founded by Palestinian refugees.

Islamic State has also taken over swathes of Iraq and has claimed attacks in Egypt, Libya, Tunisia and Yemen.

Hamas is an Islamist movement that shares the jihadis' hostility to Israel but not their quest for a global religious war, defining itself more within the framework of Palestinian nationalism.

Deemed a terrorist group by Israel, the United States and the European Union, and viewed by neighboring Arab power Egypt as a regional security threat, Hamas's struggle against Islamic State-linked jihadis has not won sympathy abroad.

Israel's intelligence minister, Israel Katz, accused Hamas on Tuesday of partnering with Islamic State affiliates in the Egyptian Sinai - a charge long denied by the Palestinian group.

"There is cooperation between them in the realm of weapons smuggling and terrorist attacks. The Egyptians know this, and the Saudis," Katz told a Tel Aviv conference organized by the Israel Defense journal.

"At the same time, within Gaza, ISIS (Islamic State) has been flouting Hamas. But they have common cause against the Jews, in Israel or abroad."

(Reporting by Ali Abdelaty; Writing by Dan Williams and Nidal al-Mughrabi; Editing by Robin Pomeroy)