Catalysis of the reaction: S-adenosyl-L-methionine + histone H3 L-lysine (position 4) = S-adenosyl-L-homocysteine + histone H3 N6-methyl-L-lysine (position 4). This reaction is the addition of up to three methyl groups to the lysine residue at position 4 of the histone H3 protein.
histone-H3K4 methyltransferase activity