Nonperturbative renormalization group potentials and quintessence

New solutions to the nonperturbative renormalization group equation for the effective action of a scalar field theory in the local potential approximation having the exponential form e(+/-phi) are found. This result could be relevant for those quintessence phenomenological models where these kinds of potentials are already used, giving them a solid field theoretical motivation. Other nonperturbative solutions that could also be considered for the quintessence scenario are also found. Apart from this particular cosmological application, these results could be relevant for other models where scalar fields are involved, in particular for the scalar sector of the standard model.