We report the results of a new search for long-range spin-dependent interactions using a Rb-^{21}Ne atomic comagnetometer and a rotatable electron spin source based on a SmCo_{5} magnet with an iron flux return. By looking for signal correlations with the orientation of the spin source we set new constraints on the product of the pseudoscalar electron and neutron couplings g_{p}^{e}g_{p}^{n}/ℏc<1.7×10^{-14} and on the product of their axial couplings g_{A}^{e}g_{A}^{n}/ℏc<5×10^{-42} to a new particle with a mass of less than about 1 μeV. Our measurements improve by about 2 orders of magnitude previous constraints on such spin-dependent interactions.