According to its Unique Trait description it builds melee combo multiplier for whatever your equipped melee weapon is.
Tested with the following frames:
Wukong
Excalibur Umbra
Valkyr
Baruuk
Map: Adaro (Sedna) - Exterminate - Steel Path - Solo
Armaments: Primary: Rauta; Secondary - Lex Incarnon; No standard melee equipped
Method: Start mission, generate sufficient energy using Zenurik to activate Exalted Melee weapon for frame (exception for Baruuk, his 1, 2, and 3 were used to generate sufficient resource to utilize Desert Wind). Once Exalted Melee was activated, one full magazine of the Rauta was fired into the nearest enemy at close range ensuring multiple pellet hits, then the melee weapon was used to observe if there was any change in combo count. None was observed with any of the warframe's exalted weapons listed above.
If this behavior is intentional, it should probably be included in the weapon's trait description even if it would be very disappointing for it to be case.