Summary Due to geographical factors, it is impossible to build large‐scale communication network infrastructure in remote areas, which leads to poor network communication quality in these areas and a series of delay‐sensitive tasks cannot be timely processed and responded. Aiming at the problem of limited coverage in remote areas, the space‐air‐ground integrated networks (SAGIN) combined with mobile edge computing (MEC) can provide low latency and high reliability transmission for offloading delay‐sensitive tasks for users in remote areas. Considering the strong limitation of satellite resources in the space‐ground integrated network and insufficient energy of local user equipment, firstly, a satellite‐UAV cluster‐ground three‐layer edge computing network architecture is proposed in this paper. Under the condition that the delay requirements of various ground tasks are met, the task offloading problem is transformed into a Stackelberg game between ground user equipment and edge servers. In addition, it is proved that the existence of Nash equilibrium in non‐cooperative game between ground user equipment by using potential game. Finally, a Nash equilibrium iterative offloading algorithm based on Stackelberg game (NEIO‐SG) is proposed to find the optimal offloading strategy for tasks to minimize the system offloading cost and the optimal forwarding percentage strategy for offloading tasks to maximize the utility function of the edge server. Simulation results show that compared to other baseline algorithms, NEIO‐SG reduces the total system latency during task offloading by about 13 and the energy consumption of the edge server by about 35.