Neither related to nor to be confused with demure.

demurral (de·mur·ral): / di MUR uhl /
noun

(1) a mild objection or refusal; an indication of hesitancy; an instance or act of demurring

[Literally demur + -al.]

Usage: His polite demurral of their offer to give him a ride to the next town revealed more than a hint of fear.