We investigate properties of the ground-state and first radially excited four-quark mesons X-0 and X-0' with a diquark-antidiquark structure [ud][(c) over bar(s) over bar] and spin-parities J(P) = 0(+). Our aim is to reveal whether or not one of these states can be identified with the resonance X-0(2900), recently discovered by the LHCb Collaboration. We model X-0 and X-0' as tetraquarks composed of either axial-vector or scalar diquark and antidiquark pairs. Their spectroscopic parameters are computed by employing the QCD two-point sum rule method and including vacuum condensates up to dimension 15 in the analysis. For an axial-axial structure of X-0((')), we find partial widths of the decays X-0((')) -> D- K+ and X-0((')) -> (DK0)-K-0, and estimate full widths of the states X-0((')). To this end, we calculate the strong couplings at the vertices X-0((')) DK in the framework of the light-cone sum rule method. We also use technical approaches of the soft-meson approximation necessary to analyze tetraquark-meson-meson vertices. We obtain m = (2545 +/- 160) MeV and m' = (3320 +/- 120) MeV [m(S) = (2663 +/- 110) MeV and m(S)' = (3325 +/- 85) MeV for a scalar-scalar current] for the masses of the particles X-0 and X-0', as well as estimates for their full widths Gamma(0) = (140 +/- 29) MeV and Gamma(')(0) = (110 +/- 25) MeV, which allow us to interpret that neither is the resonance X-0 (2900). At the same time, these predictions provide important information about the ground-state and radially excited diquark-antidiquark structures X-0 and X-0('), which should be objects of future experimental and theoretical studies.