  The properties of uniformly rotating white dwarfs (RWDs) are analyzed within
the framework of Newton's gravity and general relativity. In both cases
Hartle's formalism is applied to construct the internal and external solutions
to the field equations. The white dwarf (WD) matter is described by the
Chandrasekhar equation of state. The region of stability of RWDs is constructed
taking into account the mass-shedding limit, inverse $\beta$-decay instability,
and the boundary established by the turning points of constant angular momentum
$J$ sequences which separates stable from secularly unstable configurations. We
found the minimum rotation period $\sim0.28$ s in both cases and maximum
rotating masses $\sim1.534 M_{\odot}$ and $\sim1.516 M_{\odot}$ for the
Newtonian and general relativistic WDs, respectively. By using the turning
point method we show that general relativistic WDs can indeed be
axisymmetrically unstable whereas the Newtonian WDs are stable.
