Sheikh Ahmed el-Tayeb made the remarks in a meeting with Pope Tawadros II of Alexandria on Tuesday, Gate.ahram.org website reported.
Pope Tawadros II welcomed the Al-Azhar official and said such meetings will help to spread compassion that will serve the whole society.
He also stressed the need for upholding peace in family, society and the world.
El-Tayeb, for his part, congratulated the Christian leader on the arrival of the new year.
He also highlighted the importance of peace and said it is a concept that Muslims use in their prayers.
The cleric went on to say that the root of all religions is the same and people are all brothers.
Egypt is a country in North Africa with a population of around 100 million. Some 90 percent of the country’s people are Muslim.
It also has a sizeable Christian minority. Egyptian Copts are the biggest Christian community in the Arab world. Estimates of their numbers vary, but generally range between 4.7 and 7.1 million.