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Momentum and density dependence of the isovector part of nuclear mean field uτ(k, ρ) is studied by using effective interactions having general form. It is found that only the difference between finite range parts of the exchange interactions between like and unlike nucleons accounts for the momentum dependence of uτ(k, ρ). Depending on the choice of the parameters of these exchange interactions, two conflicting trends of momentum dependence of uτ(k, ρ) are noted which lead to two opposite types of splitting of neutron and proton effective masses. The behavior of uτ(k, ρ) at the Fermi momentum k=k F is related to the density dependence of nuclear symmetry energy Jτ(ρ) and effective nucleon mass M*(k=k F , ρ)/M in symmetric nuclear matter. The need for possible theoretical and experimental efforts to constrain the high density behavior of Jτ(ρ) as well as to resolve the puzzle regarding the two opposite types of splitting of neutron and proton effective masses are also stressed.