In a 6- to 8-quart heavy pot bring 3 quarts water to simmering; add mango and cook, uncovered, for 10 minutes, stirring occasionally. Drain well in a colander set in a sink. Measure 4 cups mango; return the mango to pot. Add sugar, lemon juice, and orange juice to mango in pot. Bring to boiling over medium heat, stirring to dissolve sugar. Quickly stir in pectin; return to a full rolling boil, stirring constantly. Boil hard for 1 minute, stirring constantly. Remove from heat. Quickly skim off foam with a metal spoon. Stir in lemon peel and orange peel.
Ladle hot preserves into hot sterilized half-pint canning jars, leaving a 1/4-inch headspace. Wipe jar rims; adjust lids and screw bands.
Process filled jars in a boiling-water canner for 5 minutes (start timing when water returns to boiling). Remove jars from canner; cool on wire racks.