"Я не буду дзвонити вам."

Translation: I will not call you.

[Myron1313]

Could вас be used in place of вам?

[Vinnfred]

Call = викликати - вас (genitive)
Call = дзвонити - вам (dative, think of "to give a call")

[Crookfingerjake]

Is there are difference between the two meanings?

[Vinnfred]

дзвонити comes from дзвін (ringing). It means "to ring", in both meanings: to ring a bell (in its literal meaning) and to make a telephone call.
викликати - to demand or ask for the presence of, to cause, to challenge

[mzbka]

You could say "Я не буду дзвонити до вас." if you really wanted to use вас

[kvUa13]

Can be won't?

[Weylin366674]

How do you say: Don't call me, I'll call you?
And does it have the same meaning?