Trump was quoted in a UN briefing as asking on Thursday why the United States would accept more immigrants from Haiti and "shithole countries" in Africa rather than places like Norway.
He was speaking while he was rejecting an immigration deal by the two main parties in the US Congress.
In a statement, al-Azhar said that the remarks are racist comments.
The statement referred to the growing trend of dogmatism, racism, Islamophobia and terrorism in the world and said Trump’s remarks are against the values of co-existence and cultural tolerance.
The statement also said Trump should apologize for his comments.
In the meantime, the African Union, a group representing the continent's countries, issued a blistering statement demanding that Trump retract and apologize for comments referring to African nations as "shitholes".