CAIRO, June 1 (Reuters) - Egypt has asked rival Palestinian factions for written proposals on how best to prevent internal fighting in the Gaza Strip, to be discussed by the factions in Cairo sometime in July, a source close to Hamas said.

"There's an understanding that Fatah and Hamas and the other Palestinian factions will meet in Cairo next month, and papers are expected from Hamas and Fatah and all the factions... with some proposals and understandings on solving the current internal Palestinian crisis," the source told Reuters.

The source added that that the papers would also outline each faction's proposal on how to deal with violations of any agreements reached.

Egypt has held talks in the past week with Palestinian politicians from the rival sides in a bid to ease tensions that erupted in violence in May in Gaza, holding talks with Palestinian Deputy Prime Minister Azzam al-Ahmad and separately with Moussa Abu Marzouk, Hamas's deputy politburo chief.

The source said no direct talks between Fatah and Hamas were planned. Fighting between them in Gaza killed about 50 people last month.

Egyptian officials have previously indicated their frustrations with efforts to play a mediating role in the Gaza Strip, which borders Egypt.

Egypt hosted a meeting in April between Palestinian President Mahmoud Abbas and Hamas's exiled leader Khaled Meshaal, whose groups formed a national unity government in March to try to ease friction. Yet serious fighting again broke out in Gaza in May.

A relative calm has held between them for the past few days, accompanied by a relative decrease in Palestinian-Israel fighting. Previous ceasefire deals have rarely lasted long.

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