We reconsider the derivation of the nucleon-nucleon parity-violating (PV) potential within a chiral effective field theory framework. We construct the potential up to next-to-next-to-leading order by including one-pion-exchange, two-pion-exchange, contact, and 1/M (M being the nucleon mass) terms, and use dimensional regularization to renormalize the pion-loop corrections. A detailed analysis of the number of independent low-energy constants (LECs) entering the potential is carried out. We find that it depends on six LECs: the pion-nucleon PV coupling constant $h^1_pi$ and five parameters multiplying contact interactions. We investigate PV effects induced by this potential on several few-nucleon observables, including the $vec{p}$-$p$ longitudinal asymmetry, the neutron spin rotation in $vec{n}$-$p$ and $vec{n}$-$d$ scattering, and the longitudinal asymmetry in the $^3$He$(vec{n},p)^3$H charge-exchange reaction. An estimate for the range of values of the various LECs is provided by using available experimental data.
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