The renormalization of the chiral $\mathit{np}$ interaction in the ${}^{1}{S}_{0}$ channel to next-to-next-to-next-to-leading order (N3LO) in Weinberg counting for the long-distance potential with one single momentum- and energy-independent counterterm is carried out. This renormalization scheme yields finite and unique results and is free of short-distance off-shell ambiguities. We observe good convergence in the entire elastic range below pion production threshold and find that there are some small physical effects missing in the purely pionic chiral $\mathit{NN}$ potential with or without inclusion of explicit \ensuremath{\Delta} degrees of freedom. We also study the renormalizability of the standard Weinberg counting at next-to-leading order (NLO) and next-to-next-to-leading order (N2LO) when a momentum-dependent polynomial counterterm is included. Our numerical results suggest that the inclusion of this counterterm does not yield a convergent amplitude (at NLO and N2LO).