Recently, Adaptive Traffic Signal Control (ATSC) in the multi-intersection system is considered as one of the most critical issues in Intelligent Transportation Systems (ITS). Among the proposed AI-based approaches, Deep Reinforcement Learning (DRL) has been largely applied while showing better performances. This paper proposes a new DRL-based cooperative approach for controlling multiple intersections. The problem is modelled as a Multi-Agent Reinforcement Learning (MARL) system, while each agent is trained to select the best action to control an intersection by obtaining information about its local lanes state. The cooperation aspect is manifested in this approach by considering the effect of the state, action and reward of neighbour agents in the process of policy learning. An intersection controller applies a Deep Q-Network (DQN) method, while transferring state, action and reward received from their neighbour agents to its own loss function during the learning process. The experimental results under different scenarios shows that the proposed approach outperforms many state-of-the-art approaches in terms of three metrics: Average Waiting Time (AWT), Average Queue Length (AQL) and Average Emission CO₂ (AEC). In addition, the cooperation between the different trained DRL-based controllers allows the system to continuously learn and improve its performance by interacting with the environment, particularly when the traffic is congested.