I'm looking for a word that can describe a person continuously talking angrily as if fighting with someone, for example over a phone, but in a low and whispering manner.
As already noted you could use growl:-
v.intr. 1. To emit a low guttural sound or utterance. 2. To speak in an angry or surly manner.
or possibly snarl:-
v.intr. 1. To growl viciously while baring the teeth. 2. To speak angrily or threateningly.
or perhaps hiss:-
- A sharp sibilant sound similar to a sustained s.
- An expression of disapproval, contempt, or dissatisfaction conveyed by use of this sound.
v.tr. 1. To utter with a hiss: 2. To express (a negative view or reaction) by uttering a hiss: The audience hissed its displeasure.