Fill in the blank with the correct option.

The President finally had to _________ the demands of the public for his resignation.

accede to 

The correct answer is Option (3) - accede to 

Here's why:

    Accede to means to agree to a demand or request, often reluctantly.
    Ignore means to disregard something completely.
    Initiate means to begin something.
    Condone means to tolerate or accept something that is wrong or blameworthy.

In the context of the sentence, the President is giving in to the public's pressure, not starting something new, ignoring them, or approving of their demands.  So, "accede to" best captures the idea of the President reluctantly agreeing to the public's request for his resignation.