"One cannot send a message that while hate messages against some are unacceptable, these are acceptable against others," Khan said, adding that this was "reflective of prejudice and bias that will encourage further radicalisation".
In response to Khan's appeal, a Facebook spokeswoman told Reuters the company was against all forms of hate and that it did not allow attacks based on race, ethnicity, national origin or religion.
"We'll remove this hate speech as soon as we become aware of it," the spokeswoman said in an emailed statement, adding that the company had "more work to do".
Khan, in his letter, referred to the situation in France, where, he said, Islam was being associated with terrorism.
Earlier on Sunday, Khan said that French president Emmanuel Macron had "attacked Islam" by encouraging the display of cartoons depicting the Prophet Mohammad.
Khan's comments came after Macron paid tribute to a French history teacher beheaded by an Islamist radical who wanted to avenge the use of cartoons depicting the Prophet Mohammad in a class on freedom of expression.