Summary: When facing multivariate covariates, general semiparametric regression techniques come at hand to propose flexible models that are unexposed to the curse of dimensionality. In this work a semiparametric copula-based estimator for conditional quantiles is investigated for both complete or right-censored data. In spirit, the methodology is extending the recent work of H. Noh et al. [J. Am. Stat. Assoc. 108, No. 502, 676–688 (2013; Zbl 06195970)] and H. Noh, the second and third author [“Semiparametric conditional quantile estimation through copula-based multivariate models”, J. Bus. Econ. Stat. 33, No. 2, 167–178 (2015; doi:10.1080/07350015.2014.926171)], as the main idea consists in appropriately defining the quantile regression in terms of a multivariate copula and marginal distributions. Prior estimation of the latter and simple plug-in lead to an easily implementable estimator expressed, for both contexts with or without censoring, as a weighted quantile of the observed response variable. In addition, and contrary to the initial suggestion in the literature, a semiparametric estimation scheme for the multivariate copula density is studied, motivated by the possible shortcomings of a purely parametric approach and driven by the regression context. The resulting quantile regression estimator has the valuable property of being automatically monotonic across quantile levels. Additionally, the copula-based approach allows the analyst to spontaneously take account of common regression concerns such as interactions between covariates or possible transformations of the latter. From a theoretical prospect, asymptotic normality for both complete and censored data is obtained under classical regularity conditions. Finally, numerical examples as well as a real data application are used to illustrate the validity and finite sample performance of the proposed procedure.