Catalysis of the reaction: an adenosine in mRNA + S-adenosyl-L-methionine = an N(6)-methyladenosine in mRNA + H+ + S-adenosyl-L-homocysteine. This activity is the methylation of adenines in mRNA with the consensus sequence RRACH, where R is a purine, and H is C, A, or U.
mRNA (N6-adenosine)-methyltransferase activity