The top religious authority in Sunni Islam says it hopes Pope Benedict XVI's successor will work for better ties between Muslims and Christians.
Al-Azhar al-Sharif institute in Cairo said it sought to "re-establish ties based on mutual respect and understanding".
The statement was its first response to Pope Benedict's decision to resign.
Relations between the Vatican and the Muslim world became strained in recent years after comments by the Pope.
His papacy got off to a rocky start with al-Azhar, which accused Benedict of repeatedly addressing Islam negatively.
Relations soured in 2006 after Pope Benedict quoted a 14th Century Byzantine emperor in remarks taken by some Muslims to imply that Islam was a violent religion.
Pope Benedict has repeatedly said words did not reflect his personal views, but stopped short of issuing a clear apology to Muslims.
In January 2011, al-Azhar suspended indefinitely its traditional dialogue with the Vatican in protest at what it said were "repetitive and negative statements" about Muslims by the Pope.
Al-Azhar accused Benedict of repeatedly claiming that Christians in the Middle East, and in Egypt in particular, were discriminated against and oppressed.
The Pope's statements on Christians in the Middle East came after a deadly New Year's Eve bombing in the al-Qiddissin church in the Egyptian coastal city of Alexandria three years ago.
At least 21 people were killed and 70 injured in the attack, which authorities said was carried out by a suicide bomber.
Egypt has the largest Christian minority in the Arab world. Church figures say Christians comprise about 10% of Egypt's population of 83 million people.
Egyptian Copts (Christians) have long complained about discrimination and outright oppression under former President Hosni Mubarak.
And since Mr Mubarak's overthrow in January 2011, Christian Egyptian leaders have expressed concerns about political gains made by Islamists.
Al-Azhar (which means the "most flourishing and resplendent" in English) was named after Fatima al-Zahraa, daughter of the Prophet Muhammad.
It was established in 971 as a mosque and then expanded into a university.
Over hundreds of years it has drawn millions of Muslim students and scholars from across the world.
Despite its long history and reputation al-Azhar was badly tainted by its close association with a string of Egyptian rulers, especially during Mr Mubarak's three-decade rule.