Present approximations to the correlation energy, E-c[n], in density functional theory yield poor results for the corresponding correlation potential, v(c)([n]; r) = delta E-c[n] delta/n(r). Improvements in v(c)([n]; r), are especially needed for high-quality Kohn-Sham calculations. For a two-electron density, the exact form of v(c)([n]; r) in its high-density limit is derived in terms of the density of the system and the first-order wave function from the adiabatic perturbation theory. Our expression leads to a formula for the difference 2E(c)[n] - integral v(c)([n]; r) n(r) dr, valid for any two-electron density in the high-density limit, thus generalizes previous results. Numerical results (both exact and approximate) are presented for both E-c[n] and integral v(c)([n]; r) n(r) dr in this limit for two electrons in a harmonic oscillator external potential (Hooke's atom).