I believe that Vito would be inclined to negotiate a truce sooner rather than later--war gets in the way of business. But, he was in no position to negotiate from his hospital bed or sick room, and he couldn't trust Sonny with such a sensitive task. On the other hand, Sonny was an excellent tactical warrior (the novel says he had "a genius for urban guerilla warfare"). And, since Sonny had fought the other families to a "stalemate" (the novel again), Vito could afford to let Sonny have his way with the war while he recovered and planned the family's next strategic moves.

So, I'm guessing, Sonny and Vito had an unspoken arrangement: Sonny would brief Vito from time to time on the progress of the war, Vito would say nothing, or simply nod.