Turkey's TRT news agency said the letter was delivered by the nuncio Jean-Paul Aime Gobel and the sheikh made it clear to the nuncio that the "anti-Islam discourse in the West" was their "red line" that he rejected outright.
An Al-Azhar spokesman said the visit bore "a strong message regarding the normalisation of Al Azhar-Vatican relations", which have been frozen since January 2011.
At an Angelus last month Francis referred to Muslims as "our brothers".