IS killed more than 40 people in twin church bombings in April 2017 and a month later shot dead 28 Christians in Minya province.
Church spokesman Bouls Halim said the death toll in Friday's attack south of the capital Cairo was likely to rise.
Security officials said the attackers opened fire on two buses carrying pilgrims from Bani Suef and Sohag provinces, also south of Cairo.
Egyptians check on their relative, who was wounded after gunmen attacked a bus carrying Coptic Christians, at the Sheikh Fadel hospital in Beni Mazar on November 2, 2018.
It said the attack left 13 Christians killed and another 18 wounded, but it was not immediately possible to independently verify the claim or reconcile the discrepancy in the number of dead and wounded given by the group and the church.
The bus was heading to the Monastery of Saint Samuel the Confessor located in the western desert.
Egyptian authorities have also convicted jihadists for their role in attacks against Copts.
President Abdel Fattah El Sisi released a statement on Twitter condemning the attacks. But other attacks carried out by Islamic State (IS, formerly ISIS) have been far more deadly. The previous attack in May 2017 left almost 30 people dead. "The terrorists attacked them and fled", he said.
Egypt is a Muslim-majority country and its Christian minority - mostly members of the Coptic Orthodox Church - make up around 10% of the population. Christian activists say the church's alliance with el-Sissi has offered the ancient community a measure of protection but failed to end frequent acts of discrimination that boils over into violence against Christians, especially in rural Egypt.