Network congestion is a major issue affecting communications in Connected and Autonomous Vehicles (CAVs) under high vehicle density scenarios. The common idea used by emergency message broadcast protocols to overcome this challenge is to reduce the number of retransmissions. This is achieved by suppressing redundant retransmissions while maintaining broadcast reliability. In this paper, we analyze the problem of inaccurate suppression of redundant retransmissions in delay-based broadcast protocols and propose uHBS (unHurried Broadcast Suppression), a new more efficient broadcast suppression mechanism. uHBS avoids inaccurate decisions to suppress or forward an emergency message by considering the occurrence of duplicate receptions of this message and using an indication about the channel’s busy status. Next, we use the proposed uHBS mechanism as a basis for designing uHBS-DP (uHBS based Dissemination Protocol), a novel delay-based protocol for broadcasting emergency messages in urban vehicular networks. The simulation results show that uHBS-DP, using the proposed broadcast suppression mechanism, significantly improves the efficiency of emergency message broadcasting by ensuring high reliability with low broadcasting overhead, compared to two other variants of uHBS-DP that use conventional suppression mechanisms. Furthermore, the results show a substantial improvement, compared to a well known protocol, in terms of reduced collision ratio (up to 36.57%), lower dissemination delay (up to 19.17%) and reduced broadcast overhead (up to 19.28%).