We study a new mechanism of dust accumulation and planetesimal formation in a gravitationally unstable disk with suppressed magnetorotational instability and we compare it with the classical dead zone in a layered disk model. We used numerical hydrodynamics simulations in the thin-disk limit ( FEOSAD code) to model the formation and long-term evolution of gravitationally unstable disks, including dust dynamics and growth. We found that in gravitationally unstable disks with a radially varying strength of gravitational instability (GI), an inner region (of several astronomical units) of low mass and angular momentum transport is formed. This region is characterized by a low effective value for the $ GI $ parameter, often used to describe the efficiency of mass transport by GI in young protoplanetary disks. The inner region is also similar in terms of characteristics to the dead zone in the layered disk model. As the disk forms and evolves, the GI-induced dead zone accumulates a massive dust ring, which is susceptible to the development of the streaming instability. The model and observationally inferred dust masses and radii may differ significantly in gravitationally unstable disks with massive inner dust rings. The early occurrence of the GI-induced dust ring, followed by the development of the streaming instability suggest that this mechanism may be behind the formation of the first generation of planetesimals in the inner terrestrial zone of the disk. The proposed mechanism, however, crucially depends on the susceptibility of the disk to gravitational instability and requires the magnetorotational instability to be suppressed.