This paper deals with broadcasting problem in vehicular ad hoc networks (VANETs). This communication mode is commonly used for sending safety messages and traffic information. However, designing an efficient broadcasting protocol is hard to achieve since it has to take into account some parameters related to the network environment, for example, the network density, in order to avoid causing radio interferences. In this paper, we propose a novel Autonomic Dissemination Method (ADM) which delivers messages in accordance with given priority and density levels. The proposed approach is based on two steps: an offline optimization process and an adaptation to the network characteristics. The first step uses a genetic algorithm to find solutions that fit the network context. The second one relies on the Autonomic Computing paradigm. ADM allows each vehicle to dynamically adapt its broadcasting strategy not only with respect to the network density, but also in accordance to the priority level of the message to send. The experimental results show that ADM effectively uses the radio resources even when there are globally many messages to send simultaneously. Moreover, ADM allows to increase the message delivery ratio and to reduce the latency and radio interferences.