Context : Aims : 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 . Methods : 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 . Results : 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 . Conclusions : 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 .