  We present an investigation of the interquark potential determined from the
qq^bar Bethe-Salpeter (BS) amplitude for heavy quarkonia in lattice QCD. The
qq^bar potential at finite quark mass m_q can be calculated from the equal-time
and Coulomb gauge BS amplitude through the effective Schr\"odinger equation.
The definition of the potential itself requires information about a kinetic
mass of the quark. We then propose a self-consistent determination of the quark
kinetic mass on the same footing. To verify the proposed method, we perform
quenched lattice QCD simulations with a relativistic heavy quark action at a
lattice cutoff of 1/a ~ 2.1 GeV in a range of the quark kinetic mass, 1.0 {\ge}
m_q {\ge} 3.6 GeV. Our numerical results show that the qq^bar potential in the
infinitely heavy quark limit (m_q -> {\infty}) is fairly consistent with the
conventional one obtained from Wilson loops. The quark mass dependence of the
qq^bar potential and the spin-spin potential are also examined.
