Rinse 6 clean plastic containers and lids with boiling water. Dry thoroughly.
Crush blackberries thoroughly, one layer at a time. Sieve half the blackberries to remove seeds, if desired. Measure exactly 4 cups prepared fruit into large bowl.
Mix sugar and pectin in medium saucepan. Stir in water. Bring to boil on medium-high heat, stirring constantly. Cook and stir 1 min. Remove from heat. Immediately add to prepared fruit; stir 1 min. or until blended.
Fill all containers immediately to within 1/2 inch of tops. Wipe off top edges of containers; immediately cover with lids. Let stand at room temperature 24 hours. Refrigerate up to 3 weeks or freeze up to 1 year. (If frozen, thaw in refrigerator before using.)