Ethiopian Orthodox Patriarch Mathias I landed in Cairo early Saturday on his first visit to Egypt.
Mathias I, who is to stay for six days, came to Egypt heeding an invitation from Pope Tawadros II.
The Egyptian and Ethiopian churches have played a role in smoothing negotiations between the two countries regarding the Grand Renaissance Dam Ethiopia is building on the Blue Nile.
Cairo has been concerned the dam could have an adverse effect on Egypt's water supply.
The Ethiopian church was formerly an archdiocese of the Church of Alexandria but became autonomous in the 20th century.
An Ethiopian people's delegation visited Egypt on 16 December for four days where they met officials, religious figures and intellectuals, including Egyptian President Abdel-Fattah El-Sisi and Pope Tawadros II.
Patriarch Mathias I became the 6th patriarch of the Ethiopian Orthodox Church in February 2013.