The early evolution of protostellar disks with metallicities in the $Z=1.0-0.01~Z_odot$ range was studied with a particular emphasis on the strength of gravitational instability and the nature of protostellar accretion in low-metallicity systems. Numerical hydrodynamics simulations in the thin-disk limit were employed that feature separate gas and dust temperatures, and disk mass-loading from the infalling parental cloud cores. Models with cloud cores of similar initial mass and rotation pattern, but distinct metallicity were considered to distinguish the effect of metallicity from that of initial conditions. The early stages of disk evolution in low-metallicity models are characterized by vigorous gravitational instability and fragmentation. Disk instability is sustained by continual mass-loading from the collapsing core. The time period that is covered by this unstable stage is much shorter in the $Z=0.01~Z_odot$ models as compared to their higher metallicity counterparts thanks to the higher mass infall rates caused by higher gas temperatures (that decouple from lower dust temperatures) in the inner parts of collapsing cores. Protostellar accretion rates are highly variable in the low-metallicity models reflecting a highly dynamical nature of the corresponding protostellar disks. The low-metallicity systems feature short, but energetic episodes of mass accretion caused by infall of inward-migrating gaseous clumps that form via gravitational fragmentation of protostellar disks. These bursts seem to be more numerous and last longer in the $Z=0.1~Z_odot$ models in comparison to the $Z=0.01~Z_odot$ case. Variable protostellar accretion with episodic bursts is not a particular feature of solar metallicity disks. It is also inherent to gravitationally unstable disks with metallicities up to 100 times lower than solar.
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