GAZA, Nov 30 (Reuters) - Hundreds of supporters of the Hamas Islamist group protested outside the Gaza Strip's border crossing with Egypt on Sunday to demand Saudi Arabia grant them permission to take part in the annual haj pilgrimage to Mecca.

The Saudis have granted visas to some 3,000 Gazans who registered for the haj through the Palestinian Authority, which is based in the Israeli-occupied West Bank and headed by President Mahmoud Abbas, leader of the secular Fatah faction.

But when the pilgrims approached the Rafah border crossing between the Gaza Strip and Egypt on Saturday, Hamas security forces turned them way.

A Hamas source said the group would allow those registered with the Palestinian Authority to pass through Rafah only if Saudi Arabia also granted visas to some 3,000 pilgrims who signed up for the haj with Gaza's Hamas-led government.

"We should all go or no one should go," demanded protester Masoud Abu Oamr, a 45-year-old merchant who says he registered for the haj with Hamas.

Protesters sang, "Oh God, We answered your call", a chant used during the haj in which Muslims retrace the footsteps of the Prophet Mohammad. Pilgrims from Gaza hoped to arrive in the next few days.

Tensions between the rival factions have been on the rise since Hamas boycotted reconciliation talks in Cairo earlier this month, irritating Egypt and Saudi Arabia.

A Hamas lawmaker in the Gaza Strip, Atef Adwan, drew a hostile response from Abbas aides after being quoted as saying the denial of visas to Hamas supporters could stir opposition within Saudi Arabia to the regime.

"Making such threats against Saudi Arabia reflects the extent of their isolation," senior Abbas aide and Fatah official Ahmad Abdel-Rahman said of Hamas.

Adwan later issued a statement saying he was misquoted. He said he made no comments hostile to Saudi Arabia, a powerhouse Hamas is reluctant to alienate.

A Saudi foreign ministry official responded to Adwan's reported remarks.

"Saudi Arabia looks at all Palestinians as equals and has granted thousands from all over the occupied territories, including the Gaza Strip, entry visas to perform haj," the official was quoted by the Saudi state news agency as saying.

"They (visas) were delivered to the Palestinian Authority," the report said. "All of the kingdom's entry points are ready to welcome them and facilitate for them performing the ritual." (Reporting by Nidal al-Mughrabi in Gaza and Wafa Amr in Ramallah; Writing by Adam Entous; Editing by Sophie Hares)

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