Islamic fundamentalists have routinely targeted Christians in Egypt since the 2011 revolution, however the attacks have grown in severity over recent months. The officials spoke on condition of anonymity under regulations. The gunmen then retreated and did not reach the monastery compound, which is heavily fortified and guarded by Egyptian police and security forces. Moments after the border closure last week militants from Sinai fired a rocket into Israel.
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Tuesday's attack comes just days after bombings at two Coptic Christian churches left 45 people dead.
Only monks and clergy were inside the monastery at the time, since the site, a UNESCO World Heritage Site which was once a popular destination for pilgrims, has been closed to the public since 2015, for security reasons.
One of Christianity's holiest sites came under attack, during a fire exchange between Egyptian police and ISIS gunmen at Mount Sinai. Egypt has been fighting the group in north Sinai province for several years but attacks in south Sinai are rare.
Security sources told Reuters that security had been put on high alert at touri st facilities across southern Sinai after the attack.
Egypt's Copts, the Middle East's largest Christian community, have also long complained of suffering discrimination, as well as outright attacks, at the hands of the country's majority Muslim population.
The latest attack on St Catherine's comes just 10 days before Pope Francis is due to visit Egypt.