Differential equations with discrete and distributed delays are considered. Explicit continuous-stage Runge–Kutta methods for state-dependent discrete delays based on functional continuous methods for retarded functional differential equations and Runge–Kutta methods for integro-differential equations based on methods for Volterra equations are combined to get a method suitable for both types of delays converging with order four. A method that requires six right-hand side evaluations and only two of its integral argument evaluations is presented. The questions of the practical implementation for delay differential equations within general non-smooth solutions are discussed. The numerical solution of test problems confirms the declared fourth order of convergence of the constructed method.